How do you "assume ownership" of a dead fic?

it depends on whether the writer is still around or not. If so then you can ask the author for permission to take ownership of their story, and they agree you both can goto Meeester and the admins and ask for the story to be transferred.

If the writer is dead, long gone, or unavailable, then the best you can do is attempt an unofficial sequal (you used to be able to do an unofficial rewrite of the story, but that was banned, explicitly, in the rules after the whole RC drama a couple of years back -- I miss the guy, I never got the RC rant I wanted about my story )