Is there a time limit on unsecured debt??

The recession has caused a very noticeable increase in some borderline collection practices, and chasing people for relatively ancient debts like this is one of them.  It isn't illegal, if you actually did have that account and didn't pay it.  At the same time, I wouldn't even consider paying something just on a phone call, if you don't remember the account, I'd ask for some written evidence of the debt.

However, this one is pretty far out of the ballpark.  The statute of limitations, for contract actions in New Jersey, is six (6) years, and it runs from whenever the account went into default and stayed that way -- so unless you made a payment in the last 6 years, there's no way they can sue you.  I've heard of collection people lying about that, saying it's longer.

Don't let threats of having this affect your credit frighten you, either.  Under the credit reporting laws, there's effectively an 8-year limit from default, after which a bad debt can't be reported any longer.