This is a different question, but I've occasionally wondered why some franchises (like Star Trek, Buffy, or Harry Potter) generate a lot of fanfic and others generate much less. Part of this is raw popularity, of course, but quite a bit isn't; the film Avatar (the one with blue aliens, not the one with kung fu) was far more popular than, say, Pirates of the Caribbean, but the latter spawned a thriving fic community and the former has a smattering of stories mostly intended to illustrate critical points.

I don't think there's any single answer, but a franchise's chances seem to be improved if: it's suitable for episodic storytelling (Pirates is a self-contained story, but it's framed like an entry in a serial); it's got strong and ideally archetypal characters (Kirk, McCoy, Spock: action/emotion/reason, easy to write but easy to give depth to); and it's got an open setting with a lot of depth and unexplored bits (few settings outside spec-fic generate a lot of fanfic, and most of those that do are period pieces or procedurals). We're looking at works as toolkits for storytelling, in other words; tight plotting might actually be detrimental.

I cannot parse your question. Can you rephrase?