I don't think they can sue for emotional distress really. Going after the estate of a deceased defendant isn't unheard of in civil litigation. What they can do is not to settle, and to try to prove that the deceased was the only person on the IP address who downloaded music illegally (if illegal downloading is proven to begin with). Of course blaming a recently deceased family member for something isn't exactly fun...

My guess of course is that the RIAA will try to convince them that they have no legal recourse, and that their only option is to settle out of court...

I wish we could boycott the RIAA, but that's not feasible.