Warning: at the moment, this is just an idea. I don't know if I'll do anything with it.
Summary (I absolutely stink at summaries, and also I wanted you guys to get the full picture)
There's a young woman from the real world. She loves fanfiction, and prefers fiction over reality. One day, she shifts into the world of one of her favorite stories. She stays there for a short time, then shifts to the next story. After a few shifts, she realizes that what triggers the shift is someone realizing that she's not from their reality. For example, when she goes to the world of The Hobbit, Fíli and Kíli become her best friends. She tells them the truth and shortly afterwards (usually a few hours), she shifts away. She can't control which worlds she goes to, and she can't return to any of them. She gets pregnant once, then ends up shifting. She loses the baby because she always reverts back to her original age and physical condition. She goes to the world of the Avengers and falls for Loki. He knows she's hiding something and confronts her about it, but she refuses to tell him. When he asks why, she tells him it's because the moment she reveals the truth, she loses him, she loses everything. He asks what secret could possibly be that bad. She still refuses to tell him, and asks him to trust her. He does. But he eventually figures it out while talking to her. She freaks out and starts sobbing. Now that he knows and she's about to be dragged away anyway, she tells him everything. They get a few hours wrapped in each other's arms, then she fades away as she shifts. Loki makes it his mission to find her. He goes hunting for the reality stone. It's in pursuit of the stone that he ends up playing his role in the Marvel movies. It takes a few decades, but he does get it. In the time he's been searching, she's been asleep. After shifting away, she entered a spiral of depression. She volunteered for a mission in space, knowing chances of survival were slim, and has been in hypersleep ever since. When Loki activates the reality stone, he brings her sleeping form back to his reality. After he finally manages to wake her up, they have a happy tearful reunion. She then proceeds to live a long life with him. She doesn't die of old age though, because every time someone realizes she's from another reality, she shifts away and her body resets, and he brings her back with the reality stone.
This story would probably be a series of her lives in different worlds, with the last stop being Avengers.