Can’t pay a debt after statute of limitations due to state law: what do I do now??

Recently I applied for a credit card and was pre-emptively denied because of debt on an old charged-off credit card I'd forgotten about. I called the issuing company and found out that I'd already passed the statute of limitations. I offered to pay 50% as a final settlement and they accepted. Cut to a week before the due date and I still hadn't received the offer letter I'd requested. I was told it was sent, and they transferred me to a more specialized department. That department told me that it hadn't been sent, because in fact, the state that I am living in (Wisconsin) is one of two states that prohibits me from making payments on a debt past the statute of limitations. So, as I understand it, there is nothing that I can do about the debt. If I cannot pay it, then an old debt remains on my credit report and I will continue to be penalized with a lower credit score and either being denied credit, or being charged higher rates… even though I want to pay the debt.

What can I do in this absurd case, besides leaving my life, community, and large possessions I've started building/acquiring in this state and claiming residency somewhere else? Am I destined to carry an unpaid debt and its consequences forevermore?