I let all of my print subscriptions lapse because I want to see what those publishers will do to win me back. They often have existing win-back programs in place so the rep on the phone can offer you some deal in order to get you back on board.
Publishers won’t advertise win-back programs because everyone will then know to let subscriptions or memberships to just about anything lapse. The publishers don’t want to encourage this, but need such a program on hand for that last ditch effort.
As a marketer, you can get some interesting ideas from such programs and see exactly how much the provider wants you. To a major daily newspaper, I know someone who just got the very same subscription for half off, and then the publisher sent her a bathrobe. They really needed her in order to keep their circulation figures up for ad rates.
I’ve seen this practice online, too. ISPs use it. Online retailers employ it. For example, if they know your email address and see you bail out of their shopping cart, you just might get a follow-up email enticing you to go back and buy that which you initially decided to pass on.