dead people's copyrighted work sues for copyright issues all the time... not sure how that would help.
, but often some large corporations
if the person is still alive then people might believe it's an original and the impersonated can legitimately claim that the fake is profiting from that mistaken identity.
A deepfake Elvis video of a song that he didn't write would be subject to copyright by the original author of the song and to trademark by the owner of Elvis's likeness. However, it seems plausible that such a trademark claim might fail because (among other things) it should be apparent to a viewer that it isn't actually Elvis.