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Can the parents or parent get into any legal trouble if their child runs away? - parents

First, I did not flee to, nor anyone I know. I was just curious because I do not see how it is possible that the boy was forced to leave home and live in a terrible environment (and can always sexually abused) others. Thus, parents can pay into trouble with the police or something, if the child is free to escape option? And if so, what type of action in place of the parents not the child.