The statute of limitations for medical bills is only 2 years, so you need to investigate before you do anything. If you make any payment, even $1.00, you will revive the statute of limitations.
Plus, if they are in her name only the collector has no grounds to hold your husband liable -- his ex may have a claim against him if he was ordered to pay part or all of them in the decree, but not the collector.
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You probably should consult with a local family law attorney about this.
Additionally, you should check on the statute of limitations for your area. The debts may be barred by the statute of limitations (those debts are pretty old) and to demand payment may be a violation of the FDCPA.
I would think that your husband is equally responsible for his kids' medical care. There may be something in the divorce paperwork about assigning liability but I would expect your husband (children's father) to be responsible.
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