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
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").