Victoria Schwab tells the story of a young French woman who is able to live forever, and without being able to be remembered by anyone she see. To capture the woman's Faustian bargain, the title of the book is called The Invisible Life of Addie LaRue.
Be forewarned, you will be jumping back and forth over a span of three hundred years because the novel has a non-linear timeline. Addie steals a scarf from a closet shelf this time, and then a paperback of The Odyssey next time. The thief can be caught, but never remembered. There's no need to worry about Addie's track record, when any thieving can be erased by a new page, an instant apart, and every life is a fresh start. A clean slate.
It's like getting a unlimited supply of Get Out of Jail Free cards, and everyone knows how satisfying that feels, however temporary. And then, between one life and the next, Addie can often roll a double six to Pass Go.
The ache of Addie's "life", however, can be tougher than what we could have imagined. And maybe it isn't a perfect way to live a life without being remembered. The curse for Addie to be forgotten by everyone she meets is much worse than the gain of being immortal: she isn't living any life at all when she is forgotten.