According to the Office of the Comptroller of the Currency, banks generally don't close accounts that have a negative balance, so even if you request the closure of the account while it's in a negative status, chances are the bank will not honor it. A negative balance indicates that you owe money to the bank. If the account is overdrawn due to overdraft fees, you may be able to request that some, or all, of the fees are removed. The bank may comply if the account had a good history up until that point; however, if your account has a history of negative balances, the bank may be less inclined to remove any fees for you.
The bank will require you to bring the account to a positive status to close it, either by making a deposit into the account or transferring funds from another account into the account with the negative balance. Any externally initiated deposits, like direct deposit from your job or Social Security benefits, will also contribute to lowering the negative balance, since the bank will apply all newly deposited funds toward the negative balance first. You want to bring the account current as soon as possible to avoid an increase in the negative balance.
If you allow your account to remain negative for an extended period, the bank may unilaterally decide to close the account. This will not relieve you of the financial obligation. In fact, it can make the situation worse. The bank will report the account to ChexSystems, which is the credit reporting agency for financial institutions. Most banks check the ChexSystems database before opening a new checking account and will not open an account for you if you have a record in ChexSystems, even if you've paid the amount owed. Consumers reported to ChexSystems remain in its database for five years.
The bank may place an unpaid balance with a collection agency. A collection agency will report the account to the credit bureau. Collection accounts are a negative mark on your report and can lower your credit score. Depending upon the dollar amount owed, the collection agency may decide to sue you to obtain a judgment, which gives the agency the right to garnish your wages or place a lien on your property, depending upon the laws of your state.