Elves did exist in Atmora, and even many were limited to small bands for much of history, there would be a fair number with the 1st Aldmeri Dominion.

Most of the Elves present in Atmora were stragglers, remnants, and recluses, however, some civilizations did thrive for limited epochs of time.
The notable Mer of Atmora were:

1. Balmer or 'Stone Elves': reclusive cliff-dweller mason elves of legend, they built some sites, yet many were ultimately overtaken or ruined. Some myths claim they turned to stone by their own hesitance to the forces of history.
   
2. Moramer or '[​Elder] Woods Elves': tribal Mer that lived within and about the Elder-Wood forests, particularly in trees and roots.
   
3. Aldmer ('Old Elves')
   
4. 'Gilmer / Gilemer' (or sometimes called Dsalmer) or '[​Proud] Ice/Glacial Elves': these Mer thrived about ice, yet faded with the demise of Atmora in a most mysterious manner and are thought to be related (perhaps kin) to the Snow Elves.
   
5. Falmeri / Falmer ('Snow Elves'): While Falmer did exist in Skyrim, some myths and legends regard their origin having some connection to the lands of Atmora. Those that consider such stories speculate that they may have been largely driven from Atmora early on (perhaps near the Dawn Era), yet there may have been further migrations if any occurred. There may have been attempts by certain groups of Falmer to settle, seek retribution, and/or escape into Atmora since the gradual departure of Men from the continent. The fate of any such elves is a mystery, yet probably did not fare well in the end.
   
6. Dwemer ('Deep Elves'): these Mer were often travelers & researchers which were not all native.
   

The Falmer were Snow Elves, but some fled into Dwemer settlements for shelter. Many of the Dwemer were mistrusting and turned the Elves into slaves by giving them toxic fungus to make them blind.
While a similar crisis would have been less likely to occur the same in Atmora, conflicts between other Elven and non-Elven (mainly Human) cultures could have made a similar situation possible.

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Some of the terms used for Elven races are based upon the Aldmeri language, which is explained in this Imperial Library article.