I actually haven't read this example, but I have it on my shelf for when I do get the heart to read it. >.>
The Hitchhiker's Guide to the Galaxy series wasn't completed by the time Douglas Adams died in 2005. So Eoin Colfer took it upon himself to write the sixth book and try to tie the story up. Even though I have it on my shelf, I honestly don't know if I can actually go through with reading it. To me, that series is just too personal, and Adam's voice too distinct. I don't really necessarily like the idea of other authors finishing a series after an author's death, regardless of who they are. Especially if they weren't involved in the creation of the series to begin with. It feels like a disservice.
However, there are a few instances where I can see it working. Like mentioned earlier, if the children or close partner/assistant were to finish the series, I would see where they would be able to do the story just. Anne Rice's assistant Becket and her son Christopher Rice could totally take over the Vampire Chronicles if needed (not like we're gonna need that any time soon).
However, I just don't like the idea of it. :S