Will my husband still have to pay child support after he relinquishes his rights to his daughter?

My husband has been enduring emotional abuse from his daughter's mother for 9 years now. She voluntarily took their child and left him 9 years ago as they were about to have a house built on a piece of property that they had bought. Last week Wednesday, my husband finally could no longer take the abuse he has been enduring and suffered a nervous breakdown. I had to physically put him in the car and take him to the doctor. He is considering relinquishing his rights to the child as she doesn't want to live with us and our 4 other children. She stopped communicating with us about 6 months ago, when we thwarted her mother's attempt to seal over $1,200 from us for a medical bill that she had transferred into my husband's name without telling us. We are not sure as to what is going on in their home as she will no longer talk to us about anything. He feels that it is in the best interest's of everyone involved for him to just sign his rights away.