Ideally, all banks should be provided with extra capital, in a way that is not penalising but sufficient to reassure markets that indeed no bank will be allowed to fail, even if the economy deteriorates further.
This type of recapitalisation, in excess of prudential requirements, would be a way to restore confidence in the financial system and tackle the macroeconomic problems that would emerge if banks start curtailing loans to the private sector as the preferred way to achieve the capital requirements that markets request.