An illiquid firm cannot pay today; an insolvent one cannot pay ever. They need different rescues.
A bank fails when its liabilities come due faster than its assets, which can happen to a solvent bank.
Any banking interview question on runs, deposit insurance, liquidity rules or March 2023.
From It's a Wonderful Life · 1946
A rescue that swaps assets at fair value changes nothing; only new capital changes a bank's solvency.
Banking crises, bailout design, and the interview question of what a capital injection does that asset purchases do not.
From John Hussman's October 2008 market comment on recapitalising the banks · John Hussman
Lending cures illiquidity; only capital cures insolvency. Decide which problem you have before choosing the remedy.
Questions about why Lehman was allowed to fail and AIG was not, about central bank lending, or about any distressed situation.
From Too Big to Fail · 2011