Many checking accounts charge a monthly fee if you don't maintain a minimum balance or other qualifications. However, what happens if you have a $0 balance and they can't deduct the monthly fee from your balance? (Similarly, some accounts have an early closure fee for closing an account within 6 months... but how can it be charged to you if you have a $0 balance?)
Unless your agreement says otherwise, the bank is authorized to debit your account for the amount — and then charge you an additional fee for being overdrawn. If you do not add money to the account to bring it into a positive balance, they can pursue you for it just as they could any other debt. They may also choose to close your account instead.