Yes, the bank can still demand that you pay back what you spent on the card, even if you close the account. If you read the cardholder agreement, you'll see that it explains that, and says that the interest and payment terms continue, if you close the account, for as long as you have an open balance. So you can expect, in that case, to go on getting the same monthly credit card statement, with the same monthly minimum payment, until you get it to zero.
And if you don't pay, you can expect to be sued.
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