A legal status that defines a person or institution unable to repay any outstanding debts owed to creditors.
In a banking sense this is when the banks equity capital has become exhausted and as a result they no longer have any funds available to recover losses made on their balance sheet - prompting a bank failure.
Bankruptcy most commonly occurs when the bank's assets fall in value on the balance sheet because of the presence of non-performing loans (NPLs) and this makes the bank a loss which the equity capital must cover. But the more equity capital is used up, the more vulnerable the bank becomes. Eventually (if these losses continue) the bank will run out of equity capital and it will become technically insolvent when the losses they have made on assets exceed the level of equity capital.