In the second chapter of the tantric text Two Investigations, Vajradhara says,

In the degenerate time, I, who am called Vajrasattva, will abide in the form of the spiritual master. With the aim of benefiting sentient beings, I will abide in ordinary forms.

In the tantric text Vajra Tent, Vajradhara says,

In the future degenerate times, I will manifest as a child and in various forms as a means.

In the same text, Vajradhara also mentions,

In the final five-hundred-year period, I will manifest in the holy body of the leader of disciples. At that time you should believe it is me and generate devotion.

Another tantra says,

At the end of time the All-Pervasive Lord himself will manifest in the ordinary body of the holy virtuous friend and guide the transmigratory beings of the degenerate time.

While these quotations come from tantric texts, there are also quotations from the sutras. Once on a high mountain in south India where Guru Shakyamuni Buddha was teaching, bodhisattva Amoghadarshi asked Buddha, “At the moment we can receive teachings from the Buddha, but what shall we do in the future when you have passed beyond sorrow? Who will guide us?” Guru Shakyamuni Buddha replied, “Amoghadarshi, in degenerate times in the future, I will manifest in the forms of spiritual masters and abbots. In order to ripen the minds of sentient beings, I will also show birth, old age, sickness and death. Don’t worry that you will not meet me in the degenerate times. At that time I shall manifest as the abbot or as the teacher.”

In other words, Guru Shakyamuni Buddha said that in the future he would take ordinary forms and manifest experiencing the samsaric problems of birth, old age, sickness and death. Amoghadarshi asked this question on behalf of all sentient beings and Buddha’s reply was meant not only for Amoghadarshi but for all sentient beings.

Also, in the sutra Great Gone Beyond Sorrow Buddha explains,

Even though I have shown passing beyond sorrow in this great land of Dzambu, in the end I have not gone beyond sorrow completely. Even though I have shown being conceived in a mother’s womb in this land of Dzambu, it is just for my mother and father to recognize me as their son; my holy body wasn’t born from the gathering of attachment. My holy body does not have sufferings of hunger and thirst, but in order to fit with the beings of this world, I also show hunger and thirst. Other than that, I also show myself as an ordinary being to individual beings. I have had profound wisdom for countless eons. Even though I have passed completely beyond the world created by grasping, I show walking, sitting and other conducts. I show having headaches, stomach aches, backaches and boils. I wash my legs, hands, face and mouth, and clean my teeth with a tooth stick. Even though individual ordinary beings believe I have all these problems, my holy body has none of these problems.

There are many such quotations where Guru Shakyamuni Buddha said that he would manifest for the benefit of sentient beings. Even though Buddha himself has no suffering, he manifests having suffering; even though Buddha has no faults, he manifests having faults.

Also, in the past when Shakyamuni Buddha was the bodhisattva Brahma Samudraraja, he generated bodhicitta and made five hundred special prayers in the presence of his guru Ratnagarbha. He prayed, “In the future quarreling time of the five degenerations, when the lifespan of human beings in this world will be one hundred years, I will guide and subdue the sentient beings of that time, who the other thousand buddhas of the fortunate eon found too difficult to subdue.” Buddha voluntarily took this responsibility upon himself. This quotation, usually found in the section on the kindness of the guru, can also be related to this outline.