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Suppose I have a software program I publish under a non-free license that does not give permission to create derivatives, and I own the copyright. Someone decides that despite the copyright they are going to make a derivative of it anyway.
My question:
If this happens: Do I own the derivative that the person made? Could I take the derivative and publish it under an open source license?
No, you don't own the derivative that somebody else make of your work.
Creating a derivative requires permission from the creator of the original work. One of the purposes if free culture licenses is to grant anybody this permission up front. If your work is not free (for instance, it is "All Rights Reserved"), then nobody can legally create a derivative of your work.
What you can do if somebody goes ahead and make a derivative anyway, is to sue for copyright infringement. If you win the case, you are eligible for monetary compensation, and the illegal derivative must be removed from the market - but the copyright of the adaptation is still owned by the infringer and cannot be transferred to you by any legal decision.
