You might lose the credit card rewards in your credit card account when your account closes. However, if you used a credit card to earn miles or points in an airline or hotel loyalty program, those rewards won't disappear.
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If the credit card account you plan to close is one of your oldest accounts, it will reduce the average age of your remaining accounts when it is removed from your credit report. This would potentially lower your credit score, though usually not dramatically.
It's possible that you could see your credit scores drop after fulfilling your payment obligations on a loan or credit card debt. Paying off debt might lower your credit scores if removing the debt affects certain factors like your credit mix, the length of your credit history or your credit utilization ratio.
When you close a credit card and you still owe a balance, the debt you owe doesn't go away. The card agreement still applies, and you are still legally responsible for repayment. The following will also go on as normal: You'll continue receiving credit card statements in the mail.