If I understand their lore correctly, aboleths:

* Are practically all immortal

* Reproduce constantly 

* Grow indefinitely

In other words, they're essentially Darwinian daemons but even worse. This begs the question: where do they all go? If they all stayed on one plane then they'd probably exceed the biomass of all other life in a matter of millennia. Is there any lore about this problem, or is it left up-in-the-air for other worldbuilders to deal with?

This Aboleth?

https://www.dndbeyond.com/monsters/16762-aboleth

I think the Underdark is just a big, vast place with a lot of creepy crawly hidey holes where slimy, eyeless monsters can lurk in the dark. Most aboleths probably end up in that environment. 

While they can reproduce (by fission I think) I don’t think they do it very often since they regenerate on the (infinite) plane of water with full memory. What is really needed is a way to destroy their soul/spirit/ memory so they don’t regenerate and can then be killed off potentially.

Into the future where they become mind flayers who travel to the past in order to right perceived wrongs only to come into conflict with themselves because they're now two species of xenophobic abominations?

I don't think there's ever been any lore that aboleths ever give rise to mind flayers.

Aboleths were originally native to the oceans, then were driven into the Underdark after a war with the gods. At least that’s what our DM told us.

That’s pretty much the straight lore. They are found in the depths of oceans, deep lakes, and watery regions of the underdark. They came into existence before the gods and their slave civilization was wiped out by the gods. (drawing on other lore in the MM, the gods created the krakens to wipe out the aboleths and their society/civilization. When it looked like they had succeeded they realeased the krakens who now live in the same deep waters as the aboleths.) this presents a very scary possibility- kraken are not immune to the mind control of the Aboleths, could many of them now be aboleth mindslaves? That might explain the powers of groups like the FR’s Abolethic Sovereignty. A scary thought that a CR23 critter like the kraken could be a mindslave to a CR 10 critter like an Aboleth.

Thanks. Thanks a lot. Really. 

Because now I've got THIS monstrosity stuck in my head...

♫ If it hadn't been for Aboleth Joe
♫ I'd been married long time ago
♫ Where did you come from, where did you go?
♫ Where did you come from, Aboleth Joe?

Thanks. Really.

Your welcome

Maybe that's why krakens are evil. Maybe after the war, the aboleths enthralled the krakens as part of a long plan to take back the world, waiting for the right moment to rid the inner planes of the gods.

The lore here differs from what's on the Forgotten Realms wiki, where aboleths originally hail from the depths of the far realms, and while they don't die of old age, they don't seem to return to a home plane like fiends do when not killed there. "Fantastically ancient" Aboleths have grown to about 40 ft. and a reproduction cycle takes about 10 years with 1-3 offspring.

There's two things to consider:

First is that the lore has changed between editions.

Second is that the FR Wiki is a fansite that isn't official and has plenty of entries that are made up of people half-remembering something they saw in a sourcebook 30 years ago or simply entering someone's homebrew as if it were canon.

Not to mention that all is just made up and can be what ever you need it to be currently. Deep Sea horror? Check. Extra dimensional swarm Horror? Check. Solitary Underworld Stalker? Check. Intergalactic Xenosith? Also Check!