Yes, the case should be closed, unless there is some amount of arrears which has not been collected or distributed.
Frankly, child support enforcement agencies are provided with incentive payments from the federal government to continue collecting child support. The amount is between 5-15% of the amount collected and distributed. Consequently, GA DCSS has no particular incentive to close your case, as long as there is any possibility that you may still be obligated for support.
If you are not obligated for any further support or arrears, and GA DCSS refuses to close the case, then you would have to petition the Superior Court for an order against DCSS (termed "writ of mandate"). This could be costly, and may not be worth the effort. But, it's legally possible, if you have no other alternative.
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