Yes. They can do both. If your credit card issuer suspects that you have the money to repay your account they can and will sue you. This usually happens you’re your credit card balance is $1000 or above. In most cases, if you become severely delinquent on payments, your credit card company will close your account and put it into collections. But the worst thing that can happen if you don’t pay your credit card bill for a long period of time is your credit score being destroyed. This will make it very hard for you to get approved for credit cards or any other type of loan in the future.