Okay, I'm going to give you some advice, because this can get really shady and end up screwing you in the end.
If the account has been closed for years (meaning it has already been in collections, a judgment may have been filed etc), that means that it is now going to sit in your credit report for however long it takes to get off of your credit (usually 7 years). It is debt that has been written off by the original creditor and collections agencies have bought that debt. The MOMENT you respond to this letter acknowledging the debt as yours, it will put that account into collections on your credit report. Let's say that the account in question is a decade old and it is about to fall off of your credit. If you decide to go with this "payment plan" you will reset the clock on this account, and it will stay in your credit report as being in collections. The payoff amount is always significantly higher than they paid for your debt (they usually pay the original creditor pennies on the dollar and then offer a "deal" to you to pay it off.)
If this account has been closed for many years and there has been no activity on your credit report regarding it, the best thing you can do is wait for it to fall off. Do not answer phone calls for letters from these types of companies, because once you do, the statutes of limitations no longer applies. The only people you would want to make a deal with is the original creditor or the collection agency that bought that debt directly from the original creditor if the account has just gone into collections and you want to get it off of your credit report quickly. Keep in mind, if you do reach a deal with the collection agency, they are not obligated in the least to remove the delinquent account from your credit report.
