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.
Not only did PNC bank overdraft my account due to monthly fees, they closed it because it was over drafted. I went into the bank to pay the fee and reopen my account and deposit my paycheck (from the same bank) they took their fees, would not let me re-open my account and charged me to cash my check.