Negative Balance Grows
When you can't repay the balance on your account, the bank can keep assessing fees for keeping it in the red according to its account agreement with you. Many banks will let you close or freeze the account to stop these fees from adding up, though you'll have to avoid trying to use the account for anything besides deposits in the meantime. If you do nothing, after a period determined by bank policy -- usually between 30 and 60 days but sometimes four months or longer -- your financial institution will close the account and write the funds off as a loss, though it may still attempt to collect what it is owed.
If your financial situation is dire enough for you to declare bankruptcy, some of your obligations to the bank may be wiped out. Fees associated with your overdrawn account are listed in your filing along with your other forms of debt and may be discharged. However, fees assessed after your filing may not be treated the same way. Make sure your account is frozen or closed before filing to avoid a potentially tricky fight over those charges.