It would just be for good-ole-fashion fun. Imagine what kind of crazy novella you could come up with if you had all your friends and family on facebook putting in their input on a chapter-to-chapter basis.
hahaha, oh that kind of story sounds fun actually. do we have a thread for that on here? i think I remember seeing something like that once.
That's the problem with sharing a novel online with the public--hard to get published after that. Most publishing houses even state that if the novel was put online that they will not publish it. But if you don't care about it getting published, then check out sights like webook.com or fanfiction.net or fictionpress.com The last one will give you the most chances of being read. I posted my first novel on there for a while and got like 1,500 reads, of which more than half of them read every chapter.
On another forum I've done the 'story by committee' bit, where every forum member would write a few paragraphs and the story getting weirder and weirder. But that story was meant to amuse the forum members, not to publish.