Another one of the great tumblr threads. This is the writing prompt that started it:
An old and homely grandmother accidentally summons a demon. She mistakes him for her gothic-phase teenage grandson and takes care of him. The demon decides to stay at his new home.
The version I remember reading originally is posited as a TV show. But in looking for this just know, I found another variant which doesn’t have the ending, but it has some extra episodes.
The Virtual Jackdaw 