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The distinction you are making is a lower octave of the ultimate distinction between nirvana and samsara. From the perspective of samsara, nirvana is negation and therefore dualistic and relative. Thus the Buddha says that nirvana is the door to the supermundane, not the supermundane itself, which is transdual.
This led to the distinction between a nirvana attainment that excludes samsara, and a nirvana attainment that includes samsara. One can fall back into nirvana from the former, but not from the latter. Even in the Pali Canon one finds a distinction between nibbana and parinibbana, the latter only being attained at death. From the supermundane perspective, both nirvana and samsara are illusions.
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Suffering (un-satisfactoriness) is the result of impermanence of Sensations / what is felt and Fabrication in general when Perceived through Mental Distortions when there is a gap between reality and Perception. (In many Suttas, inclusive of the latter, it is mentioned "in short 5 aggregates of clinging is suffering" but in Titthβayatana Sutta it is mentioned "Now, it is for one who feels that I make known: This is suffering ...")
Nirodha is not creating more un-satisfactoriness through Becoming or creating Fabrications by Distortion through Perception as well as Craving and Clinging.
Nirvana is unconditioned hence non dependent on anything. If it was conditioned it will be unsatisfactory as condition or its existance ceases it also ceases. This leads to a Paradox in the line of thinking in the question as when suffering ceases so does end of suffering.
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There is a connection,
If there was no suffering there is no nirodha.
Let me give an explain from a famous teaching from Lord Buddha (The Four Noble Truths)....
Lord Buddha said...
Everything is born because of reasons
Everything exist because of reasons
Things will exist only till the reasons exist
if you take them away it will not exist anymore
What are the Four Noble Truths - https://en.wikipedia.org/wiki/Four_Noble_Truths
This is the answer to your question and any such questions about connections between things.
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Although nirodha is usually translated "cessation", its main meaning is "restraint", "prevention" - e.g. of crime or any undesired activity/outcome. In modern Hindi, nirodh is even used as a word for condom.
If you really think about it, this makes sense. The way cessation of dukkha is achieved is through non-attachment - i.e. non-creation of conditions that make arising of dukkha
possible. In other words, non-attachment is prevention of dukkha
.
Prevention of X does not depend on existence of X.
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I don't know if the word "dependent" is 100% correct. I would say suffering is the supporting condition for cessation.
From Upanisaa Sutta