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Sorry it's late but is it ruby gloom?
I second ruby gloom. She lives with death.
I'm not the OP but I'm 100% sure that this is The Ancient Magus' Bride, so please, people, stop bumping this to say it's Ruby Gloom. (it's not even an anime wtf)
From what I've seen of the work page and the cover of the manga, Ancient Magus's Bride seems likely.
I'm looking for this anime where a girl with red, short hair that lives in the same house of a monster with a skull head. Do you know the name?