“Cat Skin” is a short story by Kelly Link, included in the collection My Mother She Killed Me, My Father He Ate Me, published 2010. Link says in her paragraph at the end of the tale that this is a brand new fairytale, based on on none in particular, but owes a debt to “Catskin“, “Donkeyskin” and “Rapunzel“. Link also acknowledges the influence of Angela Carter and Eudora Welty. I see similarities to Spirited Away.
“Cat Skin” is a trippy story and probably has many interpretations. This is what I get out of it, anyway.