I did an experiment on worlds beyond 2000 years, back in 31.05, I think. Total annihilation of sapient life only occurred in one instance; a small world with a very high number of megabeasts. (I think this was when BC's were utterly unbeatable..) The first thing that happened when taking my first step in Adventurer Mode was: "You have reached the Age of Emptiness!" So, yeah xD
The more usual result of a 2000~year old world was that one or two civilizations survived while all other fell. If two survived, they usually were located on the other far end of the continent, or on another continent altogether. The surviving race or races were normally humans with high numbers and spread across the map, as well as dwarves. Goblins got usurped in the usual way in every single instance, and the elves... The elves were finished off early during worldgen, or happened to survive to become complete badasses by the virtue of becoming legendaries in their own infinite lifetime.
The large majority of civilizations fell by war, or more commonly, "the 882nd Rampage of Ivo Armoredlion". After the surviving civilization(s) were left alone and undisturbed they eventually fell into some kind of stasis. These communities had the luck of not being close to the invulnerable BC's, so not even rampages showed up on the Timeline in Legends. I had some worlds were only a sole elf civilization survived, and
nothing happened after their last neighbours fell in year 1000. Absolutely nothing in 1000 years up to 2000. Civilizations with mortal citizens would of course die and become parents and take up positions and so on.
I expected the civs to at least spread throughout the world, but no new settlements or roads were built. That's the complacent and apathetic future for ya!