Avoid these calls.
In many cases, old debts that were 'written off' by a lender, credit card company, bank or hospital have been "sold" to another party. If the 'debt' the are referring to hasn't shown up on your credit report, IGNORE THESE CALLS.
For instance, say you defaulted on $1000 credit debt several years ago. You somewhow settled with the creditor and they wrote the debt off. Now, they get somebody who is willing to pay, say, $300 to THEM for YOUR 'settled' debt. They do this in the bet that you'll cough up $1000 or even $500 to 'settle' it (again). So they call you. They hound you. THey say they are with a collection agency. At this point you still owe NOTHING. It's settled right? So say you get tired and are scared and you listen to them. They say something like "Well, you still owe this debt and if we can start getting payment on it, even $10 a month, to pay it off, it will 'clear your credit'.
WRONG. Once you agree that the 'debt' is back and reinstated, you are STUCK! You basically agreed to pay them $$$ for a debt that was already writen off!!!
It WILL show up on your credit again and you'll get hosed by these jerks, especially if you decide AFTER the fact you do not want to pay them.
If you KNOW all your debts are settled, HANG UP ON THESE GOONS! Do NOT talk to them, do not take their calls and TELL THEM TO STOP CALLING YOU. If they do not, contact the Better Business Bureau and possibly a lawyer if they continue to harass you.