Might the parent succeed in arguing for the application of MCL §§ 722.1521 - 722.1532 (Uniform Child Abduction Prevention Act)? Of course given the title of the Act one would say it should not apply since given the usual definition of the word "abduction" this is not an abduction situation. The kid wasn't kidnapped, after all, he or she just ran away. But the Act has a rather broad definition of abduction, which "means the wrongful removal or wrongful retention of a child." And in turn wrongful removal and wrongful retention are defined as follows:
(o) "Wrongful removal" means the taking of a child that breaches rights of custody or visitation given or recognized under the law of this state. Wrongful removal does not include actions taken to provide for the safety of a party or the child.
(p) "Wrongful retention" means the keeping or concealing of a child that breaches rights of custody or visitation given or recognized under the law of this state. Wrongful retention does not include actions taken to provide for the safety of a party or the child.
So a "keeping" of the child that breaches custody or visitation rights counts as an abduction. Might not harboring a run away count as keeping the child in breach of custody and visitation rights? After all, one does not have to take the child to meet the definition of abduction, simply keeping him or her is enough. That would open up the possibility for the parent to go to court to seek an order under the Act to force the return of the child.
Whether that would work or not I have no idea. But a parent could try it and see what the court says. A good argument made by a persuasive lawyer might carry the day.