Can you explain how cessation of existence is known to be possible?

Conditionality is a fundamental to the Dhamma because, among other things, it allow us to explain the kind of questions you're making.

In order for emergent phenomena, entity or property to arise, all its necessary and sufficient conditions have to be in interaction in a specific way. If those conditions are not interacting in this manner, the particular emergent phenomena, entity or property would not come to be.

What the Dhamma does, among other things, is the change in the type and content of the information that constitutes a person's worldview. With sufficient training in the Eightfold Path, that change in information will result in a change perception, and naturally, the taints of greed, aversion and delusion will cease to have its informational conditions that allowed them to be. With the cease of the taints, there comes the cease of dukkha.

As you can see, nothing of the above implies a miraculous vanishing of nothing, but a gradual change of kinds and content of information and of the effects that information has on a person's thoughts, speech and bodily deeds.

Toss a pebble into (or, "a frog jumps into") a pond. That creates waves on the surface of the pond. Those waves may eventually disappear again.

I'm not sure what the physical explanation is, for that physical phenomenon of (relative) stillness returning -- is it Turbulence, becoming Heat? Surface Tension? Entropy? Dilution? -- but that (i.e. waves disturbing the surface of a pond) seems to me an analogy of something's "appearing and disappearing".

Even then the analogy may be too ideal or invented, made-up. Is a real pond ever really still? Or is that an invention, an idealisation, the sort of simplified assumption which physicists are accustomed to working with?

I once read a joke about a post-scientific society understanding Newton's inverse square law of gravity -- the "attraction between two objects is proportional to the inverse square of the distance between them" -- as being a statement about young love (i.e. "lovers close together are attracted to each other"). That's a joke because it's really meant to be a law of physics, and completely unrelated to psychology.

I'm not sure that Physical principles (e.g. "Conservation of Energy") or analogies translate well to the realm of Buddhism. For example if you have a fleeting desire, where did it go? Does a desire have any energy, i.e. as measured in Joules -- can a desire move mountains, anything like that -- or cause a rock to float, perhaps?

Part of what disappears in Buddhism is "ignorance", isn't it? Where does that "go" or cease to exist? It's not a physical thing.

The other thing is, that what "ceases" are sankharas. It's not that they "cease to exist" entirely, exactly, but they come apart, they're unmade. What happens when you burn a wooden cart -- where is the cart then, and where is the wood?

Doesn't the existence of water in a mirage cease to exist when one approach near and investigate? In the same way ignorance disappear with the light of wisdom.

The Buddha teach annihilation of ignorance to end suffering.

The Buddha does speak about an end of the world;

"And what is the ending of the world? Dependent on the eye & forms there arises eye-consciousness. The meeting of the three is contact. From contact as a requisite condition comes feeling. From feeling as a requisite condition comes craving. Now, from the remainderless cessation & fading away of that very craving comes the cessation of clinging/sustenance. From the cessation of clinging/sustenance comes the cessation of becoming. From the cessation of becoming comes the cessation of birth. From the cessation of birth, then aging & death, sorrow, lamentation, pain, distress, & despair all cease. Such is the cessation of this entire mass of stress & suffering. This is the ending of the world. Sn12.44

The world here is defined thus;

Whatever in the world through which you perceive the world and conceive the world is called the world in the training of the noble one. Sn35.116

If this is reconciled with the definition of All;

The Blessed One said, "What is the All? Simply the eye & forms, ear & sounds, nose & aromas, tongue & flavors, body & tactile sensations, intellect & ideas. This, monks, is called the All. [1] Anyone who would say, 'Repudiating this All, I will describe another,' if questioned on what exactly might be the grounds for his statement, would be unable to explain, and furthermore, would be put to grief. Why? Because it lies beyond range."sn35

Then he is here shown talking about an end of All, given that the eye, ear, nose, tongue, body & the intellect are explicitly called a world and the seen, heard, smelled, tasted, sensed & ideation are conceived & perceived by that which is explicitly called the world.

I think at this point it can be inferred that as far as the conception & perception based on the six senses goes that is as far as the law of conservation goes.

Therefore one only has to show that conception & perception based on the six senses is dependent on requisite causes & conditions and that it does not occur without causes & conditions to show that All can cease if the causes cease, one who argues that it is impossible & it cannot happen that the causes would cease would have to prove otherwise if the dependent origination is shown.

Therefore even if the All is conceived & perceived as indestructible due to causal requisites it can be explained that with the exhaustion of causal conditions the conception & perception of All would cease no matter how it is conceived.

Sutta gives this analogy for the dependent origination & cessation;

"Very well then, Kotthita my friend, I will give you an analogy; for there are cases where it is through the use of an analogy that intelligent people can understand the meaning of what is being said. It is as if two sheaves of reeds were to stand leaning against one another. In the same way, from name-&-form as a requisite condition comes consciousness, from consciousness as a requisite condition comes name-&-form. From name & form as a requisite condition come the six sense media. From the six sense media as a requisite condition comes contact. From contact as a requisite condition comes feeling. From feeling as a requisite condition comes craving. From craving as a requisite condition comes clinging/sustenance. From clinging/sustenance as a requisite condition comes becoming. From becoming as a requisite condition comes birth. From birth as a requisite condition, then aging & death, sorrow, lamentation, pain, distress, & despair come into play. Such is the origination of this entire mass of suffering & stress.

"If one were to pull away one of those sheaves of reeds, the other would fall; if one were to pull away the other, the first one would fall. In the same way, from the cessation of name-&-form comes the cessation of consciousness, from the cessation of consciousness comes the cessation of name-&-form. From the cessation of name-&-form comes the cessation of the six sense media. From the cessation of the six sense media comes the cessation of contact. From the cessation of contact comes the cessation of feeling. From the cessation of feeling comes the cessation of craving. From the cessation of craving comes the cessation of clinging/sustenance. From the cessation of clinging/sustenance comes the cessation of becoming. From the cessation of becoming comes the cessation of birth. From the cessation of birth, then aging & death, sorrow, lamentation, pain, distress, & despair all cease. Such is the cessation of this entire mass of suffering & stress."an4.174

The meaning of this imo is made quite obvious in the context of Einstein's thought experiment of the moving train and two lightnings which makes it quite obvious that as far as objectification by senses goes that is as far as conception & perception of the world goes.

In the thought experiment we conceive & perceive two conceptions & perceptions of the world occuring in the world and the two are not the same & are occurring independently of one another.

It can be reasoned that if one did not occur then perception & conception of the worĺd would not occur for this or that person but the world would not be destroyed in as far as it is still perceived & conceived by another, thus laws of conservation would be obeyed and a cessation of a world in a definitive sense would've occurred.

It can also be inferred that postulating an ultimate frame of reference that is independent of an observer would objectify non-objectification.

When requisite conditions for that in the world which conceives & perceives the world are extinct, then the world is extinct and it does not matter if it is conceived as indestructible due to laws of conservation because these too only go as far as conception goes.

Therefore this shows that there can be a cessation of a world in a definitive sense in as far as the requisite conditions for a consciousness are extinguished, there being no consciousness established there is no interference-observation & no collapse of the wave function can occur.

SN22.55 "Were someone to say, 'I will describe a coming, a going, a passing away, an arising, a growth, an increase, or a proliferation of consciousness apart from form, from feeling, from perception, from fabrications,' that would be impossible.

"If a monk abandons passion for the property of form ...

"If a monk abandons passion for the property of feeling ...

"If a monk abandons passion for the property of perception ...

"If a monk abandons passion for the property of fabrications ...

"If a monk abandons passion for the property of consciousness, then owing to the abandonment of passion, the support is cut off, and there is no base for consciousness. Consciousness, thus unestablished, not proliferating, not performing any function, is released. Owing to its release, it stands still. Owing to its stillness, it is contented. Owing to its contentment, it is not agitated. Not agitated, he (the monk) is totally unbound right within. He discerns that 'Birth is ended, the holy life fulfilled, the task done. There is nothing further for this world.

If cessation of existence, an abandoning of all being with no fuel for a future is possible, then how is it logically acceptable?

You are welcome to try showing how "something turning into nothing" is not a fallacy if you want to try that.

There's no proof needed because the premise was already wrong to begin with. There was never really "something" to begin with! It's ignorance and delusion that cook up a concept or a label of "something" from a bunch of nothings, ie. due to ignorance, there's notion of a "Ruslan" entity, a "something" other than just the Five Aggregates of form, feeling, perception, volition, and consciousness. So, no, Buddhism never proposes "something turning into nothing" for the simple reason that that "something" was never really truly exist. Once ignorance, delusion, and craving have been removed, the law of conservation of energy won't be violated, for the Five Aggregates would simply be returned to their natural entropy state. They just won't come together to form subsequent bundles of Aggregates called Ruslan, or Peter, or Jane, or whatever in the future simply because the glue and the bonds (ignorance, craving, hatred, etc.) were completely broken.

This is what the Blessed One said. Having said this, the Fortunate One, the Teacher, further said this:

“Form is like a lump of foam,
Feeling like a water bubble;
Perception is like a mirage,
Volitions like a plantain trunk,
And consciousness like an illusion,
So explained the Kinsman of the Sun." ~~ SN 22.95 ~~

In the original Pali, the word usually translated as "existence" is "bhava".

Bhava means individual existence, that is, existence as something or someone, existence in a particular way. Bhava means identification with certain form of existence: "this is how I exist, this is my way of being, this is my form, this is my bound".

Cessation of bhava is exactly cessation of this small-minded thinking. It is cessation of attachment to a certain mode, cessation of identification with it, cessation of self-limitation, cessation of bounds.

When you no longer define yourself, you no longer demand the world to be a certain way. When you don't expect the world to be a certain way - there is no basis for suffering to arise.

What remains is the bliss of suchness.

The experience is somewhat similar to the bliss of reciprocated love: just like when you abandon your fears of being who you are in front of your beloved, and for the first time can be deeply authentic and spontaneous with the person you love, whose judgement is important to you - similarly, when you abandon any and all definition of self and (its mirror reflection) the wishing for the world to be a certain way, in other words when you drop the deeply rooted fear of something going a wrong way, then, for the first time in a long time (and maybe the first time ever!) you can be completely and perfectly free from second-guessing yourself, free from the fear of judgement, free from all comparison and categorization, free to spontaneously express the sheer vast open precious immovable unmistakable unshakable joyful truth of being what you truly are.

I'll use the analogy of the Lute Sutta.

You hear beautiful music coming out of a lute, a stringed musical instrument. If you break it down into its constituent parts, you cannot find music anywhere.

Similarly, reification (papanca) creates the idea of the self, and also the idea of all the non-self things and their relationship to the self. When the existence of the self i.e. the mental idea of the self ("I am the thinker" - from Snp 4.14) ceases, then suffering ceases.

The music in the analogy is the self. The lute in the analogy is the being or satta (Vajira Sutta), an assemblage of the five aggregates.

The different parts of the lute are like the five aggregates of form, feeling, perception, mental formation and consciousness. Similar to how different parts of the lute work together to make music, the five aggregates work together according to dependent origination to build up and keep functioning the existence of the self, which is just a mental idea.

By cultivating wisdom, one eventually attains Nirvana, uprooting ignorance. Dependent origination is like a row of cards, the first of which is ignorance. When ignorance falls, the five clinging aggregates (SN 22.48) cease, hence the tainted version of mental formation, consciousness, name-and-form, six sense bases, contact and feeling, all fall. However, the (non-clinging) aggregates remain, which is what is meant by the Nibbana element with fuel remaining in Iti 44. With this, craving, clinging, becoming / existence, birth (the idea of a self) and suffering (aging, death and this entire mass of suffering) all fall and cease.

So, in this case, the lute remains, but no music comes out of it anymore. It may make sounds (i.e. the operation of the five aggregates), but it does not make sweet music (the self) any more. The arahat can feel the physical sensations of pain and pleasure, but does not suffer from them. The arahat can also have intentions and plans, without being tainted with defilements and the three poisons.

When the arahat's physical body dies, it's referred to as Nibbana element without fuel remaining in Iti 44. Here, the lute is broken into pieces and no sound comes out of it anymore. The five aggregates are no longer experienced. Also, the appearance of a being (satta), the assemblage of the five aggregates ceases. This is an emergent phenomena.

Back to the original analogy of the lute - when you break down the lute into its constituent parts, you cannot find music. There is no single thing or object such as music. It is simply an emergent phenomena that appears when different parts of the lute work together.

Upon Nirvana, what disappears is the emergent phenomena of a self - a mental idea, and also the rest of the reification of non-self mental ideas that relate ideas of the world to the self. Nothing concrete gets destroyed. No single object or thing that can be isolated gets destroyed.

Upon the physical death of the arahat, what disappears is the emergent phenomena of a being (satta), the assemblage of the five aggregates.

What is an emergent phenomena? If you arrange pebbles on a beach to look like a human face, then from the sky you can see the emergent phenomena, which is the form of a human face. But if you look closely, it's just an arrangement of pebbles.

To say that there is a concrete object called music or in this case the self - is eternalism. To say that there is no music at all or in this case, no self at all - is annihilationism. Instead, we explain the emergent phenomena of music by way of how it emerges from the inter-working of the different parts of the lute. Similarly, we explain the emergent phenomena of the self by the inter-working of the five aggregates, by means of dependent origination. This is discussed in the Acela Sutta.

Just like music, the lute is also an emergent phenomena - it is composed of various parts. Similarly, the self and the being are also emergent phenomena.

The self understood as an emergent phenomena, is the concept of anatta (not-self). The self and being understood as emergent phenomena that is objectified and classified by the mind into concrete things, is the concept of papanca (reification).

"Turning something into nothing" combines eternalism (something) and annihilationism (nothing). Instead, the explanation above takes the middle way of dependent origination and emergent phenomena.

Another analogy similar to the lute analogy is that of the scent of a flower in Khemaka Sutta.

A similar discussion occurs in the Yamaka Sutta on whether the Buddha ceases to exist after death. There it is proven that Buddha as a person is also an emergent phenomena that is not something concrete or something that can be isolated as a single object or thing.

Addendum based on discussions in the comments:

As answered by Andrei, "existence" in "cessation of existence" refers to bhava. Sometimes also translated as "becoming".

This is on the chain of dependent origination after clinging and before birth (the mental idea of the self). Cessation of existence is really cessation of the mental idea of the self, which is a reification, along with the reification that objectifies and classifies things into non-self objects according to their relationship to the self.

It's the cessation of the mental ideas that lead to suffering, which is next on the chain of dependent origination after birth. "Cessation of existence" is not cessation of the non-clinging aggregates. Of course, when ignorance ceased, the clinging aggregates ceased.

For e.g. a piece of cooked meat. To a non-vegetarian, it's delicious food. To a vegan, it's a disgusting thing. If the vegan becomes a arahat, he drops thinking "I am a vegan", "this is my car" and he sees cooked meat as what it really is, rather than associating with his self-identity.

These mental ideas are reification of emergent phenomena, that leads to suffering. The cause of it leads back down the chain of dependent origination all the way to ignorance.