If the family member is available, you should sit them down and gather up everything that they have written and have them organize and document what is there. Get all the copyright documents together, collect the stuff that is unpublished, label the tapes, etc, etc.
This is really important, because this stuff can be recorded again, published, released again, reworked into something new, etc, etc, and you want to make sure you've got it legally and physically protected, because your documentation may be the only documentation that there is--
Knowing that something was recorded, that is was copywrited, or that it was published is not enough--you've got to be able to get your hands on the specifics. The best archives, ASCAP(at ASCAP.com) Harry Fox, and the others, don't list everything that's been registered, and, even what they do list is by title, and things can have different titles. Beyond that, old recordings, songbooks, newspapers, etc can establish rights, even when the pieces weren't registered--
A few years back, I had the dubious pleasure of hearing a melody very much like one that I'd composed recorded, and forgotten, years before, coming out of a radio. Only thing was, the master had long since disappeared, the lead sheets hadn't been saved, and the only thing I had were some lyrics, and they were not the ones that had been used.
And if this story seems questionable to you, you won't be suprised to know that the it didn't make much impression the music publishers either--