“The custodial parent fills out the form with the info for the biological missing parent, and the state seeks reimbursement for the aid. It doesn’t matter that it has been 10 or 15 years, the obligation is still there.”
This doesn’t sound right. I’m pretty sure they cannot obligate anyone for anything prior to the filing date. No ex post facto laws, no bills of attainder are allowed under our constitution. (Obviously, just because a law is unconstitutional doesn’t mean it won’t be passed before being overturned. But what you describe should long since have been reviewed.)