I heard a rumor about a divorce case where the husband offered the wife a 25% higher settlement if she would leave the state. She declined. But it got me wondering. Can a valid divorce settlement or other contract provide payment in exchange for not living in a particular state? If payment is made, and the paid party doesn't move out of the state, or moves back, does the paying party have a good case to get back the payment?
A divorce settlement must be approved by the court. A Judge might well refuse to approve a settlement with such a provision in it, although I do not know of any law specifically barring such a term.
But once the settlement is final, one party could certainly offer a separate contract to the other, under which one party would agree to remain outside the state (or metropolitan region, or county, or wherever) in return for an agreed recurring payment. There would be no compulsion to accept such a contract, but if the payment offered was large enough, it might be accepted voluntarily.
However, if there was a child involved, and such a move would significantly hinder that child's contact with both parents, and this were not in the child's best interest, such a contract might be attacked as against public policy.