I'm not sure what you're trying to say. Tolkien's cosmology is clear that, by the time of The Lord of the Rings, elves are not able to live outside Valinor. If they leave the protected enclaves created by the rings of power (Elrond maintains Rivendell by using Vilya; Galadriel maintains Lothlorien by using Nenya), they will be overcome by ennui and "die".[1]

Elves do not physically die, but they will enter comas and their souls will appear in the house of one of the Valar. The Silmarillion records this happening to one elf whose comatose body is maintained (but unresponsive) while their soul can be visited and conversed with.

[1] This fails to explain how the Mirkwood elves can live there. But the answer appears to be that they can't, since they leave along with the other elves.

Original phrasing implied a sort of depressed suicide. In a figurative sense not the in world mechanics

That seems... accurate? The elves leave Middle-Earth because, when they stay in Middle-Earth, they are prone to spontaneously dying because they just can't bear to deal with being alive. "Losing the will to live" is a literal description of what happens to them, but "depressed suicide" isn't far off.