It may be morbid, but it's something every published author, at least, should think about. For the unpublished, the chances are that an unfinished manuscript isn't going to be of any value, and no one will lose any sleep or money if it's handled in a less than optimal manner, but for a published author, who's got a partial (or several partials) in the works for a contract, you should discuss with your literary representative (who should be named in your will) how you want your unfinished works handled.
There's been a fair amount of litigation over the years, when famous authors died, and the question of unfinished manuscripts arose. Most of the authors, that I recall reading about, wanted their unfinished manuscripts burned, but their executors, for various reasons, went ahead and published them, which generated all sorts of work for lawyers, and lots of angst for the heirs.
Two lessons: make sure the person making this decision is someone you really trust to do as you ask, and make sure to have a will naming a literary representative, so the court doesn't end up appointing someone who will ignore your wishes.
Unless, of course, you really don't care, because you're dead. But usually people do, in fact, care what happens afterwards, because they care about a) their literary reputation, and/or b) maximizing the profits for their heirs.