All of our regular subscriptions do auto-renew, so once you've received all of the boxes you've paid for, the system will automatically charge you again. This will continue to happen until you cancel your subscription. Cancelling will only prevent future renewals from going through, but will not affect the boxes that you have already paid for.
Our gift subscriptions, however, do not auto-renew! They simply end once your giftee has received all of the boxes that you purchased for them. (Gifts never expire before all those boxes have been received.)