Money Girl explains what the statute of limitations is on debt, and details 4 options to help handle your old, unpaid debts.

How Long Old Debt Stays on Your Credit Report
Even if you pay off a delinquent debt or the statute of limitations expires, most debt will not be removed from your credit report until 7 years after the date it first became past due.
When it comes to unpaid debt, be sure you don’t confuse the statute of limitations with the length of time that it stays on your credit reports. These are 2 completely different time limits, and are often misunderstood.
The credit reporting time limit is the maximum amount of time the credit bureaus can include negative information - such as late payments and accounts in collection - on your credit report. It’s generally 7 years, except for certain types of bankruptcies, which can remain there for up to 10 years.
So even if you pay off a delinquent debt or the statute of limitations expires, most debt will not be removed from your credit report until 7 years after the date it first became past due.
See also: Best Tips to Improve Your Credit Score
4 Options to Consider for Old Debt
If you have an old, time-barred debt, you may wonder if you should pay it. I recommend weighing your options carefully, and even speaking with an attorney before choosing one of the following 4 options:
Option #1: Pay Off the Debt in Full
Even if the statute of limitations has expired on an old debt, you may still decide to pay it. Many people believe that they have a moral obligation to pay their debts, even after struggling through a financial hardship.
I can’t make that decision for you, because everyone’s life and financial situation is different. You’re the only one who really knows if you truly can or can’t afford to pay a debt.
When it comes to your credit reports, as I previous mentioned, paying off an old debt doesn’t make its history disappear. An account less than 7 years old will remain on your report, even if it’s paid in full. However, the current status changes from “unpaid” to “paid,” which can help improve your credit.
Option #2: Settle the Debt for Less
If you want to pay a debt but don’t want to pay the full amount, many collectors are willing to settle for less. For instance, if you owe $10,000, you might offer to pay $6,000 in one lump sum, or $8,000 over time in a series of payments.
The creditor is likely to negotiate as high a settlement as possible, so always start with a low initial offer. Then make sure you get the agreed-upon terms in writing before you make any payment.
A settlement agreement should state that your partial payment settles the entire debt in full and releases you from any further obligation. If you don’t get this in writing first, your payment could be considered a partial payment, reviving the statute of limitations in some states.
When you settle a debt, the account will show as “settled” on your credit report for the remainder of its 7-year history. This indicates that the debt was not paid in full, as originally agreed, and will have a negative effect on your credit scores.
So remember that settling a debt is better for your credit than leaving it unpaid, but it’s not as good as paying it off in full.
See also: Settle Debt or Pay in Full--What's Better for Your Credit?