Yes, it is possible to "terminate" the child support obligation. However, beware that there a few judges out there that will not sign off on the order to terminate. You should consult with an attorney that practices family law to make sure you can get this done and if not, what the alternatives are (i.e. reduction/modification).
The information provided is not advice but a legal perspective and you should schedule a consultation with the lawyer of your choice.
Some additional Is information would help attorneys respond to your specific case. For example, is there an court case pending regarding the support? Did your ex contact the AG to establish child support? Are there any existing orders or child support owed at this time?
To answer your question generally, parties can agree to a range of options regarding child support, however, some judges might request more information regarding the decision to terminate support before signing off on the agreement, since support is usually in the best interest of the child.
Legal disclaimer: The response above does not form an attorney-client relationship, nor is it intended to be anything other than the authors educated opinion.
If the AG has already picked up the case, they don't care if she wants support or not. They will take the case to trial if she refuses to ask for support and the judge will order it. But this also depends on the attitude of the local office. I practice in northern Texas. It might be different in Harlingen.
If there is already a child support order in effect, the only way it goes away is if the child dies, gets married, joins the military, turns 18+graduates from high school.
What are the ages of the children? She can sign a termination of child support but if she is on any kind of benefits with the state, the AG will not drop the amount that covers the state benefits. Be aware that most judges will not sign off on that unless you have a really good reason. You definitely should hire an attorney to help you through this process if she really wants to do this. The Judge will probably make her come to court to explain her reason.
Sign up to receive a 3-part series of useful information and advice about child custody law.