Back in 2008, as the financial crisis was unfolding, there was a big argument as to whether the crisis was a "liquidity crisis" or a "solvency crisis". It's a very important distinction. A "liquidity crisis" is when banks (or similar finance companies) are financially in the black - their assets are greater than their liabilities - but they can't get the cash to keep paying their bills in the short term. A bank run is the classic example of a liquidity crisis - even if the bank could eventually pay everyone back, it can't pay them back all at once, so if people get scared and all try to withdraw their money in a rush, they force the bank to collapse. A "solvency crisis", on the other hand, is when finance companies are actually bankrupt, and no amount of short-term borrowing will change that fact.
This question has important policy implications in a financial crisis. If companies are illiquid but solvent, you just need to have the Fed lend them money to tide them over until liquidity comes back. If they're insolvent, you either need to bail them out, or help them into an orderly bankruptcy, in order to reduce systemic risk caused by disorderly failure.
Some prominent thinkers have endorsed the idea that the 2008 crisis was a liquidity crisis, created by a "run" on repo securities. People who have promoted this idea include Gary Gorton, Robert Lucas and Nancy Stokey, and John Cochrane. The model they have in mind is the Diamond-Dybvig model, the classic model of bank runs. Instead of people rushing to the bank to withdraw their deposits, the idea goes, repo customers conducted a fire sale of repo securities, preventing banks from being able to borrow short-term.
But others disagree. They claim that the reason banks' liquidity dried up was simply that the market realized that the banks were insolvent - that the mountains of housing-backed securities on the banks' balance sheets was in fact worth a lot less than most people had previously thought. These dissenters include Paul Krugman, (who favored bank nationalization), and also Anna Schwarz. They also implicitly include those who think that "Too Big to Fail" was at the heart of the crisis. If the crisis was caused by banks taking excessive risks because they knew they would be bailed out in the case of insolvency ("moral hazard"), that implies that the big banks we bailed out were, in fact, insolvent. The "TBTF" argument has been advanced by proponents of stricter regulation, including Simon Johnson and James Kwak, Paul Volcker, and Jeffrey Lacker.
In a recent blog post, Steve Williamson endorses the "TBTF" argument:
One view is that the fragility is inherent to financial systems. This view is framed in some versions of the Diamond-Dybvig model, in which the maturity mismatch and illiquidity inherent in banking imply that bank panics are possible. An alternative view is that the fragility is induced...a too-big-to-fail financial institution understands that it is too-big-to-fail, and therefore takes on too much risk, relative to what is socially optimal...This high level of risk could be reflected, for example, in a high-aggregate-risk asset portfolio, or in a maturity mismatch between assets an liabilities...[I]t is possible that Lehman Brothers could have taken corrective action...to ward off failure, if it had correctly anticipated that a bailout would not occur.
Though Williamson allows for the possibility that 2008 might have been mainly a liquidity crisis, he doubts that it's of the Diamond-Dybvig type. This is because repo is not like bank deposits, which are callable (they have "sequential service"); with repo, there needs to be some other reason for a liquidity-killing fire sale. Williamson says that he hasn't seen a convincing example of such a model. Basically, he thinks the idea that moral hazard caused a solvency crisis seems more plausible, and that the "liquidity crisis" people haven't made their case yet.
What do I think? Well, I haven't seen a "convincing" theory either, in the way that Diamond-Dybvig convincingly models the bank runs of the pre-Depression crisis. I've seen a number of interesting models, including this one by V.V. Chari and Patrick Kehoe (see also this more in-depth paper by Park and Sabourian). So I think there could be something to the "bank run" theory. It also seems possible to me that solvency crises - excessive risk-taking that blows up - could be caused by a lot more things than TBTF. For example, bubbles could create unrealistically low perceptions of risk throughout the system. Or there could be other corporate governance issues, such as incentives for excessive risk-taking by financial industry executives and traders.
Also I suspect that illiquidity and insolvency aren't as distinct phenomena as we usually think. There is ample evidence that liquidity risk is incorporated into asset prices, and there are a number of theories that try to explain this. Something that causes banks to take too much fundamental risk - TBTF moral hazard, bubbles, etc. - might also cause them to pay high prices for assets prone to sharp drops in liquidity.