It is entirely possible to have backgrounds that do not depend on specifics of the character (or limited characteristics), but they can not be as detailed as one where more information is known about the character.
But why not?
Because you literally have to avoid making any kind of references to the nature of the character. If you don't know the name of a character, they always have to be addressed with a title or nickname. If you don't know the race or class, that similarly restricts what kind of stories and interactions they can have.
Backgrounds can be based on a profession, etc, and apply to any race or gender, or there could be multiple permutations that took race and/or gender into account, but they could not be as detailed as if they were written for a specific character.
