Professor Gregory Connor:

The assets of banks tend to be illiquid long-term loans. That is what banks do. On the other side - their liabilities and the money they owe - are short-term liabilities such as, for instance, deposit savings accounts where their liability claimant often has very quick access. If depositors come to the bank and want their cash now against long-term assets, then that is called a liquidity problem. The bank needs to have cash for its long-term valuable assets. An insolvency problem is when the value of the long-term assets has fallen. For instance, many of the property loans may be failed projects and do not have real cash value. The claims made by the savers and bondholders of the bank are larger than the value of the assets of the bank. That is insolvency. It is not that the bank cannot pay cash now as its central bank can always provide. It can never pay the cash. Someone is going to have to take a loss.