I have to say, it's very frustrating when an author is unable to finish their story! Frank Herbert's "Dune" saga was finally completed recently by his son and a co author after they found his original notes and outlines; fans had to wait a couple decades after his death to see it finished.
Robert Jordan recently passed away after publishing an 11 book fantasy saga with only one installment left to go--not surprisingly, his fans exprienced no small amount of anguish (I believe he made arrangements to have it finished while his health was failing).
With anonymous internet stories, you just never know. I want to know how "A slave for Tracy" ends but probably never will. I don't post stories I haven't finished (which is why I've only posted one :P).
I didn't mind when some fans held a contest to see who could best finish John Willie's "The Magic Island," as they made it clear what they were doing and made sure to pay tribute to the late author.
On the other hand, when a writer takes it upon themselves to write sequels to "Gone With the Wind" or "The Godfather," and publishes for profit, I dunno; it seems very pretentious.
If somebody were to come up and say "Hey, I loved that story, but I can't contact the author; this is how I would finish it, and I'll remove it if they ask" and makes that clear in the story intro, would it be acceptable? Just curious.