I have a Sears credit card that I haven't used in 14 years. They have recently contacted me and told me that if I don't make a purchase by Nov. 30, that they will cancel my credit card. If they (not myself) are canceling my account that hasn't been used in years, will that hurt my credit score?
A large part of your credit score is the average age of your credit history. So if you have, say, four cards with ages of 14, 10, 9, and 3 years, your current average is 9 years, which is pretty good. If you were to close the 14-year card, then your average drops to 5.5 years, which isn't as great.
If you have a lot of credit lines and they're all as old or older, than it probably wouldn't matter as much.
Also, losing that credit line would drop your total credit line, which can affect your utilization percentage, another factor in your credit score. If your total credit line is 20k and you use 2k of that, that's 10% utilization, which is decent. If you then close a card that is 10k, reducing your total credit line to 10k, then your utilization becomes 20%, which isn't good.
If the credit line of the 14-year-old card isn't a large percentage of your total credit line, then it wouldn't affect it much.
Here's a good breakdown of the components of your credit score