Actor Bruce Willis (of all people) raised this question as well. The answer is to know the Apple ID and password of the deceased's account. As louishen pointed out, if you know the admin password, you can likely recover the Mac App Store account info that way, and carry on using and updating the app with that -- effectively giving you a second iTunes (Mac App Store, iBooks, etc) account.
There's nothing wrong with that of course. Eventually, as with all things, the apps will become irrelevant or unsupported or unused and you won't have need of the account any more.