Can a registered sex offender live in Mexico while they are on parole?

To my understanding a person on parole can travel into Mexico as long as the terms of their parole allows it but can they actually live in Mexico? And more specifically, would a registered sex offender on parole be allowed to live in Mexico?
Update: Thank you for your answers....my question is more if the U.S. would allow them to live in Mexico while on parole? They would live in a border town and would cross into the U.S. daily to work but since they'd be on parole I don't know if the U.S. parole officer would allow that?
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