Citibank pulled this crap with me recently. So after 19 years without a late payment, I ditched them.
Didn’t cancel the card, just put it in the safe until it expires. Let them send me zero balance statements for a couple years.
Good move.
Most won't send zero balance statements but if you can put, say, an 11 cent credit on one by a slight overpayment they will have to keep sending the statements. At least in my experience they don't refund negative balances less than a dollar.
That'll work until they decide to start charging you annual fees. Also if you want to cancel the card you can't just call them up and say "cancel the account" because they will lie to you and tell you they will and then they won't. You need to request that they send you a written statement, via U.S. Mail, telling you that they have cancelled it. They must comply with that request.