That is a good question.  There are many factors to consider, so I would recommend consulting a professional.
Given that, first you want to validate all the information the creditor has given you.  Look at Statute of Limitations for your State.  Review your credit reports. Get the terms in writing.  I suggest hiring an attorney to do this. Keep in mind the creditor is an adversary, they are not on your side.  Explore how many debts you have?  You could be stuck with a musical chair– you may negotiate two or three credit/medical debts and then get stuck with the last creditor refusing to negotiate.  Also know there are IRS consequences.  The debt forgiven, depending on the amount, can be taxable.  Ask the creditor how it will appear on your credit report and how long it will stay on your credit report.  Often times,  Bankruptcy is the right option to obtain a fresh start.