Legal Question in Family Law in Nevada

Probably not; almost certainly, they enjoy absolute statutory immunity. It is also possible that you have assumed facts that are not "facts." Specifically, that a voluntary relinquishment of parental rights terminates a duty of support, which in Nevada is apparently not so. See materials and discussion posted on http://www.willicklawgroup.com/child_support and http://www.willicklawgroup.com/termination_of_parental_rights.

While Nevada does not have such case law, courts in at least two other States have ruled in the past few months that even an involuntary terminations of parental rights does not extinguish the statutory duty of child support.