Such a condition would be too subjective in my opinion and subject to politics and cronyism [but I repeat myself]. There should be no "emergency liquidity". The bank should declare bankruptcy as would any other business.
For decades, emergency liquidity through the FDIC has been the norm in US commercial bank failures. The core of the 2008 crisis though involved Wall Street investment banks that were not chartered as commercial banks, so the policy innovation was in providing emergency liquidity based not on a system of deposit insurance but on Wall Street's systemic importance and to prevent failures of insurers and pension and investment fund in the US and Europe.