If I remember right, Fan Fiction is a sort-of copyright grey area. The characters are owned by the original company, but the remaining working is owned by the fan. Neither side has full ownership, and technically, publishing or sharing it (without both side’s permission) is copyright infringement.

Now, for use of existing intellectual property, the rules are the same. The difference is that anything generated by AI isn’t made by anyone, and thus can’t be owned. As such any IP owned by the company is owned by them, but anything unique from the AI is public domain.