What is MN 116 ( paccekabuddha sutta) about?

Isigili Sutta is about Pachcheka Budhdha. More information on Pachcheka Budhdha or Pachcheka Bodhi can be obtained here.

The storyline behind the Sutta is about a mountain formation (pabbatha) where many Pachcheka Budhdha lived. People saw monks (Isiwaru) going to this area but none of them returned as they became Arhath in Pachcheka Bodhi, and chose to live and pass away in the same place. So, people who lived in the surrounding area thought that the mountain rage is dangerous and called it Isigili Pabbatha (mountain that swallows Isiwaru/monks - Isi (monks) + gili (swallow) = Isigili).

This sutta is quite different to other sutta as it names many Pachcheka Budhdha who lived in the Isigili Pabbatha. None of them starved to death. They simply did not chose to come out of the mountain range (probably the mountain range was lush in vegetation throughout the year and could provide sustenance for the monks who lived there).

The Pachcheka Budhdha and Samma Sambudhdha are different in the capability to teaching and making someone else understand the Dhamma realized by the Budhdha. Please read my previous answer here, to gain more details on the differences.

The Isigili entry in the Palikanon Buddhist Dictionary of Pali Proper Names states the following. According to Buddhaghosa, the Isigili mountain was simply the dwelling place of the Pacceka Buddhas and they did come out of the mountain to get alms.

One of the five mountains round Rājagaha and one of the beauty-spots of the city (D.ii.116). There was, on one side of it, a black stone called the Kālasilā. This was a favourite haunt of the Buddha and the members of the Order. See e.g., Viii.ii.76, where Dabba Mallaputta is asked by monks to provide for them accommodation there; see also Vin.iii.41.

It was also the scene of the suicide of Godhika and Vakkali (S.i.121; iii.121f) and of the murder of Moggallāna by the brigands (J.v.125f; DhA.iii.65). .....

In the Isigili Sutta (M.iii.68-71) the Buddha is represented as saying that while the other mountains round Rājagaha - Vebhāra, Pandava, Vepulla and Gijjhakūta - had changed their old names, Isigili retained its former name and designation.

Five hundred Pacceka Buddhas once resided in Isigili for a long time; they could be seen entering the mountain, but once entered, there was no more sign of them. Men, observing this, said that the mountain swallowed up the sages and so it came by its name of Isigili (Isī gilatī ti = Isigili).

Buddhaghosa adds (MA.ii.889) that when the Pacceka Buddhas returned from their begging rounds, the rock would open like a folding door to admit them. Within the rock they had made for themselves cloisters, dwelling-houses, etc.

Venerable Nāgārjuna says:

Not the one and not another, unending and impermanent --

of the many Buddhas' transformative teachings, this is that sweet nectar's taste.

For if a Buddha is not born in the world, or if the Buddhadharma is completely extinct,

all of the wisdom of the Pratyekabuddhas would separately arise (from this).

(MMK XVIII.11-12 Madhyamakaśāstra T 1564.23c16)

The commentary from Venerable Vimalākṣa explains that "unending" refers to how, even in the age of Dharma-extinction, there are still the Pratyekabuddhas who attain Nirvāṇa. It is "unending" because it is not dependent upon a Samyaksaṃbuddha to proclaim it. Moving ahead to the section that analyses the lines about the Pratyekabuddhas:

The words of the many Buddhas are transformative teachings with the taste of sweet nectar. In worldly speech, it is like when they talk of drinking the elixir of heavenly nectar and never growing old, falling ill, and dying, (and being) without any degeneration or distress. The true aspect of the many phenomena is the taste of the true nectar. The Buddhas say that the true aspect is in three families. When the true aspect of all phenomena is attained and all of the vexatious afflictions end, this is called the Dharma of the Śrāvakas. With the arising of great compassion and the emanation of the unexcelled citta, this is called the Great Vehicle. When a Buddha has not arisen in the world, when there is no Buddhadharma, the wisdom of the Pratyekabuddhas arises separate from these. If the Buddha has already taught and entered nirvāṇa without remainder, if his Dharma has entirely degenerated in the world already, if there are those to attain the way, they but meditate upon giving up in disgust the causes and conditions for suffering. Alone, they wander into the mountains, into the woods, (wandering) away from trouble and disturbance, and they attain the path. These are called the Prakyekabuddhas.

(from the commentary)

From the OP inquiry:

So what is MN 116 about? Do the silent Buddhas enter the mountain to end life, such as starving to death?

Turning to an EBT, the Mahāsāṃghikas preserve a version of the story of Ṛṣigiri (lit. "the Sage Mountain," the Pāli is "Isigili") which suggests a distant passed-down memory of a group of Pratyekabuddhas (or sages who came to be remembered as, described as, "Pratyekabuddhas" by subsequent generations including the Buddha) who practiced self-immolation atop it. The passage is similar-enough between the versions. The Buddha recounts that Ṛṣigiri mountain near Gṛdhrakūṭa was once home to a community of Pratyekabuddhas. Once they entered the great mountain...

At that time, all the Pratyekabuddhas would, amidst the ākāśa, burn their bodies to reach Parinirvāṇa.

(EĀ 38.7 Ṛṣigirisūtra T 125.723b06)

The "ākāśa" here (空) refers to "the sky," and my tentative suggestion is that "the sky" here means "the summit of the peak" (i.e. "amidst the sky").