Indeed, this is a common misunderstanding of the status of fanworks. Most fanfics likely violate the copyright of the IP they’re based on, but that doesn’t mean that they aren’t themselves original copyrighted works. The original IP’s rightsholders can’t simply claim the fanfic’s copyright for themselves. It likely means that each party would need the other party’s permission to make legal copies of the fanfic.

This is why most studios or authors will refuse to even read unsolicited ideas that are sent to them, they don’t want to end up in a bind if someone sends them a fanfic that’s got elements in it that they already intended to use in future books or episodes and then sues them for “stealing” their work.