Company X writes checks for more than its bank balance and sends them to its vendors. When the checks get back to Company X's checking account, Company X's bank will have two options when Company X's checking account does not have sufficient funds to cover the checks:
1. The bank could pay the checks and allow Company X's checking account to be overdrawn. (Some call this an unauthorized loan by the bank.) Company X then has the obligation or liability to repay the bank for the courtesy extended to Company X.
2. If Company X's bank does not pay the checks because the account has insufficient funds, the bank will return the checks as NSF (not sufficient funds). These checks are returned through the banking system and eventually the bank of the payee will take the amount of the check from the payee's checking account. The payee will in turn reinstate the liability amount owed to it by Company X. In essence Company X did not eliminate its liability to the payee by issuing a worthless check.
Hopefully these two bank options illustrate why accountants will report a negative cash balance as a liability.
By the way, checks not paid by the bank on which they are drawn are said to have "bounced" or are called "rubber checks" since they are bounced back through the banking system by the bank on which they were drawn.