Hi - my name is XXXXX XXXXX I'm a Family Law
litigation attorney here to assist you.
Generally, a person who is incarcerated can file a motion to suspend child support payments during incarceration in order to prevent a delinquency. Also, when he gets out jail, he can ask the court to arrange child support payments to resume and re-establish visitation with the child.
Usually, courts don't hold this against the incarcerated parent, and your son should be able to contest this petition to terminate his rights. Also, terminating his rights has nothing to do with child support. Even if his rights are terminated, he would still owe child support for the child. The only time that the parent's obligation to stop child support payments to a minor is if the child is adopted.
Thus, your son should not go back to prison for refusing to have his rights terminated. However, he could go to jail for being behind on child support - but that fact is not going to change regardless of whether he has his rights terminated.
Your son can certainly contest having his rights terminated, and he should also file a motion with the court to suspend his child support support payments until he is released. That will allow him to avoid delinquency and pick up with payments after he is released.