The most profound of functions that central banks around the world engage in is being the lender of last resort (LOLR). At its core, it means that the Fed stands ready to lend to banks during times of financial trouble that, absent the Fed’s lending, would cause large-scale damages to other banks or the functioning of the financial system overall.
Provided it does not place (excessive) risks with the Fed, the textbook way for a central bank to fulfill the LOLR task is usually summarized as lending freely, on good collateral, at a high (sometimes “penalty”) rate of interest. Varyingly known as Bagehot’s “rules,” “principles,” “maxim,” or “dictum,” the meaning of the policy has been for central banks to lend freely to illiquid but not insolvent firms. That is, central banks ought to assist temporarily illiquid firms, but not help propping up fundamentally insolvent ones.
Of course, it is doubtful whether solvency can even be meaningfully established in the midst of a financial meltdown, or at which prices a bank’s assets ought to be taken — pre-crisis, post-crisis, some long-run fundamental value, or the mark-to-market price that, in extreme liquidity conditions, no longer exists? Such decisions make distinctions on both sides of the solvency line very blurry, arbitrary, and often meaningless — and allow central banks quite a lot of leeway in making decisions of when to extend emergency lending.