Not a rescue for the failing. A backstop for the sound institution that’s merely, and temporarily, out of cash at the worst possible moment.
“Lender of last resort” is a specific 19th-century central-banking doctrine, associated with Walter Bagehot’s 1873 Lombard Street though the phrase itself traces earlier to Francis Baring in 1797: a central bank should lend freely to banks that are solvent but illiquid during a panic, at a penalty rate, against good collateral, with the terms announced well in advance — protecting the money supply as a whole, not any specific failing institution. The doctrine explicitly excludes insolvent institutions, which the classical version says should be allowed to fail.
The phrase has since drifted into general use as a stand-in for “final backstop of any kind,” which loses the doctrine’s actual discipline: the whole design is conditional (solvent, not insolvent; illiquid, not broke) and priced (a penalty rate, not a bailout), not an unconditional safety net.
Source: Rochet, J.-C. & Vives, X., “Coordination Failures and the Lender of Last Resort: Was Bagehot Right after All?,” Journal of the European Economic Association, 2004; Humphrey, T.M., “Lender of Last Resort: The Concept in History,” 1989.