Seems to me that his death nullified the contract he had with Yahoo.
Actually, the easiest out for Yahoo is to have someone "leak" the mailbox contents to the family. Blame it on a rogue staffer who has been "punished"(3 lashes with a wet noodle) and be done with it.
That would still expose Yahoo! to tremendous legal liability if the family were offended by the contents of the box and decided to sue them.
This is a tough one.