what they mean by “closing” might not be what you think it means. I’ve had several credit card accounts closed over time; I voluntarily closed the last one myself. That doesn’t necessarily mean you have to pay it right this minute or have it go to collections. It usually means you simply can’t use that card for any new purchased or transfers. The amount you owe is still there, your payment plan is still there, and you just keep making payments until the balance is zeroed out. Having the account close may drop your credit score a little but it’s not like having an account go to collections. More like having a medical bill – you already got the benefit of that service, and now you’re paying the balanced owed. No more, no less. Most banks will close accounts of any kind for non-activity after a certain period of time, so this isn’t a surprising new strategy for them.
If your payments with these folks are on schedule, I’d suggest simply continuing to make payments on schedule. If you had stopped making payments for whatever reason, simply re-establishing a payment plan may be enough to make them happy (that won’t necessarily re-open the account but it will prevent it from going to collections.) If you WANT to pay it off sooner for your own reasons, then do so. But don’t rush around and feel forced to change something if that’s not already something that is of benefit to you.
Just remember that any account getting regular payments is also going to be reflected on your credit score, in your favor. Those regular payments count more in your favor, than closing off new purchases on a card that you’re not using anymore anyway. Just don’t feel rushed to do something; closing a credit account is not a huge deal.