With over 350,000 submissions of FanFiction, Harry Potter is not surprisingly the first FanFiction I read. I went on to fanfiction.net, where thousands of books, TV shows, movies and comics were being continued in every direction by fans. At first I thought the concept was kind of weird, because too many people were creating new stories and ideas for any comprehensive continuation of any one story. But then I started to read the Harry Potter FanFiction. As a dedicated fan myself, although much of the fiction was poorly written and uncomplicated, it was really intriguing to see where different people would take the story. One was based on Draco Malfoy being drunk, while another was Harry going to a school other than Hogwarts for a year. Your imagination starts to run at full speed with so much material. I know people are sad when a single book or series ends, so fan fiction seems like the perfect solution for this disappointment. From the Babysitters Club to Tom Clancy, both far-fetched and predictable continuations are made concrete by fans.
If I were to write one myself, I think I wouldn't bother writing specific stories. I think I would go ten or twenty years into the future after the actual ending and maybe write a chapter outlining important events or changes in each character, including what was going on with them at that moment. Kind of similar to J.K. Rowlings epilogue of Harry Potter, which I thought was a really smart idea so that no one could attempt to completely make up their own continuation.