While closing a credit card account, they may keep it in limbo for awhile in case any other charges come in that you authorized. Check for any automated payments from that account, or subscriptions, memberships, or creditors that might draw from that account are discontinued or switched to a different account.
Don't expect closing the account to necessarily get you out of something you signed up for, but expect to be discontinued by just closing the credit card account. Make sure you specifically cancel anything that would charge to the account.