Occurs when a bank becomes technically insolvent (liabilities > assets) and all of the equity capital for the bank has been exhausted i.e. it no longer has any equity capital to act as a buffer stock and absorb losses that the bank makes.
The process of a bank failure is as follows: The bank's assets fall in value on the balance sheet because of non-performing loans (NPLs) and this makes the bank a loss which the equity capital must cover, but as the equity capital shrinks the bank becomes more vulnerable on its balance sheet. Eventually (if these loses continue) they will become insolvent when the losses they have made on assets exceed the level of equity capital.