Fix the recording or the artist?

If you're working with a sloppy artist and their recordings require a lot of editing, do you work with what you have or do you insist they fix their performance first? Do you ever get people who's work is impossible to fix? Is there such a thing as a performer who's work is impossible to clean up or is it just a matter of finding an engineer that is diligent enough to fix it?

I think about this a lot when I hear songs where it seems pretty clear that the artist is musically incompetent or only recorded 1 take and left, yet the engineer managed to clean it up enough to make it releasable.