My husband has went through a bad custody case this last year and a half, the mother of the two children that are involved wants to wipe her hands clean of this and doesn't want to have to pay child support nore back support, how does signing your rights over work.
My question is will she still be entitled to have visitation?
What is the meaning of signing over your rights as a parent.

Have you and your husband been married for at least one year? Are you wanting to adopt the children? If you answered yes to both of those questions then get a lawyer to draw up the papers. The mother can then sign to allow the adoption and she would no longer have any rights or responsibilities to the children. However, if you answered no to either of the questions then the answer is "she can't". Simply put a parent can not just sign away their rights with out another party wanting to adopt and be qualified to adopt (the married for a year thing). She can choose not to visit and have no contact but she can't just sign over her rights unless you are wanting and able to adopt. I hope that answers your question if not please ask another one and I'll be happy to answer.

stinawords has nailed this, as has about 10,000 other similar posts and most likely 10 or 12 new posts today with basically the same question.

If there is not a step parent to adopt, the non custody parent can sign where they don't get any visits, don't have any say in raising the child, but they always have the right to go back to court later and ask for a change.
The will also have to pay child support but then they could trust the non custodial parent not to go after any support. ** unless they get state aid and then the state goes after them.

The only real way this is done ( without there being some seroius reason, danger to child, long term prison sentence or so on)