I don't know where you are getting all your information, but it's wrong.
Actually, what they are trying to get you to do is give them written acknowledgment of the debt and a new payment plan which starts the SOL from scratch and gives them 6 years to sue you for any new default.
If you are already in default for several years, don't do it.
Indiana Code
34-11-2-11 - Contracts in writing OTHER that for the payment of money is 10 years.
Indiana Code 34-11-2-9 - Contracts in writing for the payment of money is 6 years.
Indiana Code 34-11-2-7 - Accounts and contracts not in writing 6 years.
Illinois Code 735 ILCS 5/13-205 - Unwritten contracts - 5 years
Illinois Code 735 ILCS 5/13-206 - Written contracts - 10 years.
Your creditor has plenty of time to sue you.
An Illinois creditor could claim that it has 10 years to sue you in spite of you living in Indiana but I don't think that's going to fly. My guess is that the creditor would make sure to sue you within the 6 years of your default.