What is Bank Failure?

Legal Definition
A bank failure occurs when a bank is unable to meet its obligations to its depositors or other creditors because it has become insolvent or too illiquid to meet its liabilities. More specifically, a bank usually fails economically when the market value of its assets declines to a value that is less than the market value of its liabilities. The insolvent bank either borrows from other solvent banks or sells its assets at a lower price than its market value to generate liquid money to pay its depositors on demand. The inability of the solvent banks to lend liquid money to the insolvent bank creates a bank panic among the depositors as more depositors try to take out cash deposits from the bank. As such, the bank is unable to fulfill the demands of all of its depositors on time. Also, a bank may be taken over by the regulating government agency if Shareholders Equity (i.e. capital ratios) are below the regulatory minimum.

The failure of a bank is generally considered to be of more importance than the failure of other types of business firms because of the interconnectedness and fragility of banking institutions. Research has shown that the market value of customers of the failed banks is adversely affected at the date of the failure announcements. It is often feared that the spill over effects of a failure of one bank can quickly spread throughout the economy and possibly result in the failure of other banks, whether or not those banks were solvent at the time as the marginal depositors try to take out cash deposits from these banks to avoid from suffering losses. Thereby, the spill over effect of bank panic or systemic risk has a multiplier effect on all banks and financial institutions leading to a greater effect of bank failure in the economy. As a result, banking institutions are typically subjected to rigorous regulation, and bank failures are of major public policy concern in countries across the world.
-- Wikipedia
Legal Definition
When a bank cannot pay its debt and must close. Overlegeraging is the cause of this. Any deposits made by customers are insured by the FDIC insurance.