The Alwars (also spelled Azhwars) are a group of 12 ancient Vaishnava saints who lived in Tamil Nadu and are famous for their poetry in praise of Vishnu. The collection of their 4000 poems, known as the Naalayira Divya Prabhandam, is considered by many to be the "Dravida Veda", or South Indian Veda. The Alwars are crucially important figures in the history of Vaishnavism; it is the beliefs and principles embodied in the Alwars' poems that ultimately gave rise to the Sri Vaishnava sect (of which I'm a member).
In any case, the first four Alwars were known as Poigai Alwar, Bhoothath Alwar, Pey Alwar, and Tirumazhisai Alwar. Of these, the first three are famous for an occasion when they met one another. They were caught in a lightning storm, so they all went into a small cave for shelter. It soon became clear to them, however, that there was a fourth person in the cave: Vishnu. They couldn't get a good look at his face because it was dark, so all three of them started praying that the lightning would continue to strike and illuminate the face of Vishnu. It was in the course of this prayer that Poigai Alwar, Bhoothath Alwar, and Pey Alwar each spontaneously composed 100 verses in praise of Vishnu.
But my question is about when these Alwars lived. Poigai Alwar, Bhoothath Alwar, and Pey Alwar were born on three consecutive days, and Tirumazhisai Alwar was born later that year. But what's more interesting is the year: according to traditional Sri Vaishnava accounts, they were born in the Dwapara Yuga, in the year 4203 BC!
Western historians tend to dispute these dates, of course. But my question is, assuming Sri Vaishnava accounts are correct, are there any stories of the first four Alwars meeting any prominent Dwapara Yuga figures? After all, the Dwapara Yuga was the time of Krishna, the Pandavas, Vyasa, etc. Now as I discuss in this answer, Yudhisthira was born in 3229 BC, which would make him almost a thousand years younger than the first four Alwars. But people lived longer in earlier Yugas, so is it possible that they were still alive in the time of Yudhisthira and Krishna?
My guess is that they were alive during or after the time of Krishna, because their poetry evinces knowledge of Krishna; here is one of the verses of Bhoothath Alwar:
The Earth-striding lord then came as a child and drank the breast poison of the ogress with relish. My hands will salute none other than him. My lips will not praise anyone else. My eyes will not see, other than his form. Other than his names, my ears will not hear.
This is an allusion to Krishna killing the demoness Putana as a child, and considering that Bhoothath Alwar composed his verses during the cave incident, that suggests that the cave incident happened during Krishna's lifetime. So could it be that it was Vishnu's incarnation Krishna, rather than Vishnu himself, who appeared before the Alwars in the cave?