Partially an echo, in some states a garnishment constitutes a continuing lien and attaches to future deposits. If that's the case in your state, your question is understandable. Regardless, you still have the right to bring the account balance back to zero even if you must keep it open waiting in vain for some future deposit.
Ask your legal counsel.
If your state says a garnishment is only a "snapshot" and no continuing lien is involved, then closing the account is simply your prerogative. Write the customer and tell him that it's done and present him a bill for the overdraft...
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.