I know where you're coming from but I think it's jumping the gun to say that if a week has gone by without an update, it's been abandoned. I'd be hesitant to step in in those cases.

However, if an author is happy to ask for someone else to finish it, or would be happy to just post a note to say the fic has been abandoned, that would be great. But the author would have to state they're happy for someone else to take their idea and run with it.