No matter who owns your debt, the collection has to prove the debt belongs to you through a process of verification. They need to show they have the right name, Social Security number, and address on file for you and that you signed for the debt in question. Read the letter carefully to see if it indicates that the debt has been reported to the credit bureaus, and check your credit report to verify that. If it hasn’t, you can consider paying, as long as you get a letter in writing from the creditor that they won’t report it if you pay in full.
If the creditor reported you to the credit bureaus, your strategy has to be different. Ignoring the collection will make it hurt your score less over the years, but it will take seven years for it to fully fall off your report. Even paying it will do some damage—especially if the collection is from a year or two ago. The act of paying it makes the debt activity more recent, which further hurts your score.
At that point, your goal should be to exchange payment with the creditor for a letter stating they will remove the collection from your credit report. It will probably take some hard negotiation to get them to agree