My question involves a child custody case from the State of: TEXAS

If a father wishes to give up his parental rights (I understand that he will loose all and can be denied everything) and this is the very very last resort of trying to survive;

He has always paid his CS on time and is current with his payments but due to changed circumstances: loosing his job, being diagnosed with cancer and without health insurance, not having the money to pay the CS order.

He gave his ex-wife the (entire with no claims) house (+everything else)so that the children would not have to be uprooted more than necessary during the divorce.
She has since then went on to sell the house with a large profit.
And continues to make every effort to make his life a living hell.

What are the likelyhood that he will be relieved from his financial responsibilities for the children if he turns to the courts for termination of his parental rights ????????????????????