Why won't father who dodge paying child support lately sign over parental rights?

Some go to the extend of leaving the country, moving from one commission to another, one house to another, just to hide supporting their children. Most of them don't even see their children. Instead of adjectives that, why wont they just sign over their rights so they wont have to settle up.
Because under the law even if you sign over parental rights the father would still own to pay child support but he would have no endorsed standing in a custody battle or won't be capable of see them if the woman decides against. So a man loses a lot more if he signs away his rights and the kid will other resent him.

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