I don't know if it's intentionally designed into the system, or if it's just a happy accident for them. The pattern seems to be to continue charging people for things like modems and set-top boxes and hope that they don't notice for six months, and then offer to refund three months of charges as a "goodwill gesture" or some other nonsense that makes it sound like they're doing you a favor.
I haven't had this myself, but my brother cancelled his cable TV service and gathered up the equipment and turned it in to the local office. For the first couple of months, they continued to bill him full price, apparently having neglected to actually cancel his account. Unfortunately, he had given them access to his checking account, so they just took the money. When he called to complain, they said they had now cancelled his account and it would take 6-8 weeks to refund him. This happened a few times, and then they finally agreed that his account was cancelled, but then started charging him for not returning the equipment. This went on for another couple of months. In all of this, they managed to overdraft his checking account at least once. It was a mess.