The Vestige is a Soul Shriven. Soul Shriven cannot die. When they do, they will reform sooner or later. They are made out of the essence of Couldharbour and therefore linked to that realm. A bit like the lesser Daedra. Theis bodies are instable, dooming the Soul Shriven to watch their own decay for an eternity. Absorbing Skyshards will delay that process but not stop it. Elriah manages to reclaim her soul but that does not change her nature.

After the events of Summerset Elriah joins the Psijic Order. Tired of adventuring she enjoyes the peaceful atmosphere of Artaeum where she can finally leave the troubles of Tamriel behind. But before she can start to become a Psijic she first has to find a way to free a friend (no name, no spoilers) but also herself from Meridia. Meridia has imprisoned her friend in the Colored Rooms and trapped Elriah in time. While time moves forward for her it seems to stand still around her: People always speak the same phrases over and over again when speaking to her, destroyed cities are not rebuild, insteat every time she stops by they are still hammering the same nail. Even on Artaeum she is trapped while Meridia prepares a massive plot in which the Vestige is meant to play a vital role.

Since she cannot ask the Psijics for help in her situation and doesn't stand a chance to crack that problem all by herself she just travels around Tamriel, visiting all kinds of places she never visited before. At the same time her Soul Shriven nature starts to trouble her as small patches of her skin begin to shrivel and turn a pale white, wich is probably quite painful. Then eventually Meridia unfolds her plot. Which will be the final Chapter.

Once she played the hero one last time Elriah can finally move on to Arteaum. She becomes an apprentice of Sotha Sil who finds a way to stop her decay. The dacades she spends travelling between Artaeum and the Clockwork City will be the best years of her life. And then Dagoth Ur returns. Of course though, Elriah doesn't know what's going on. But over the years she notices Sotha Sil's contidion to change slowly. He doesn't share much about the troubles that plague him but when the Psijics scry dark images of the future of Vardenfell Elriah decides that something has to be done. She returns to Tamriel hoping to find some sort of weapon and gets the idea that the Amulet of Kings might be a way to start. She travels to Cyrodiil to do as much research on it as possible so that she could replicate the way it transformed souls into some sort of divine energy. But the Imperials don't trust her scientific interest and suspect that she was actually planning to steal the amulet. They throw her into prison and don't even bother about a trial. She stays locked away for several hundred years since she can't die.

As the situation in Morrowind gets worse the reigning Emperor stumbles across a certain prophecy... an orphan and outcast, a youth born on a certain day to uncertain parents. Well, Elriah is no youth but her body didn't age since she became the Vestige and she looks young enough. Also no one knows her date of birth but since there are no official documents about her such papers are even more easily forged. Before she knows it Elriah gets shipped to Seyda Neen. Her powers are mostly gone after so many years of not using them and the Psijic Order has most likely forgotten her. She wants nothing more than to go home but there was no way back. Besides, Dagoth Ur is still out there.

And the events on Morrowind happen.
Elriah tries everything to avoid becoming the Nerevarine. Destroying the Tribunal is the last thing she wants to do. But in the end she realises she cannot alway change things for the better and slowly begins to accept the prophecy.
When she leaves Mornhold at the end of Morrowind Elriah is shocked and just done with the world. She will never get her old life back and completely lost any motivation to move on.

I still need to think of how Elriah will become the hero of Oblivion and Skyrim (but it will happen!)
Moving forward.

After the events of Skyrim Elriah will live some calm years in her Lakewiev manor, sharing it with many different people, a family of outcasts. She will feel much better then and decide to join the College of Winterhold. During their research on the Eye of Magnus she will eventually find a new connection to the Psijic Order. Quaranir will not know her but she wil ask him to spread word on Arteaum. And who knows, maybe Loremaster Celarus is still out there. Maybe he will remember.