Unless some bad stuff has happened, I SERIOUSLY doubt that any judge will terminate parental rights. I know in Virginia, you cannot sign over your rights voluntarily, or even have them terminated because of child support obligations. The state looks at the best interest and the best interest of the child is to have 2 parents supporting him.
Now, since she has a husband willing to adopt, he has a chance voluntarily. They only allowed my husband because the grandparents were willing to adopt, because there would still be a two-parent home.
She won't be able to make him do it though, not unless there are circumstances involved.