It is not so critical whether the organization is formally a "bank" under a legal and regulatory definition, the economics are the same regardless.
FTX didn’t suffer a bank run. Diamond-Dybvig describes a bank trying “to call in their loans,” borrowers being “unable to pay back quickly, since their loans were, by assumption, used to finance long-term investments,” and thus “if all depositors attempt to withdraw their funds simultaneously, a bank will run out of money long before it is able to pay all the depositors” [1]. The bank was solvent. Then it was illiquid. Illiquidity finally caused insolvency.
FTX was not solvent to start with. Alameda owed them more than it was worth. The FTT position within Alameda resembles a bank run, but that characterisation is problematic since FTT wasn’t financing anything long term and was issued by an “exchange” doing fraud.
I don't think there can be.
If all assets customers have title to are held 1:1 in the currency the liability is denominated in, there is no scenario I can see where FTX is unable to fulfill customer withdrawal requests. Even if customers make use of significant margin and FTX has to liquidate all of their margin positions at once due to tanking prices. The customer who pledged their assets as collateral have now forfeited them to FTX and so have no withdrawal to make, so no liquidity crisis. The customers who did not make use of margin should have their assets sitting there ready to be withdrawn. Can you explain how a liquidity crisis can occur through margin trading?
FTX may lose significant sums of money, and face a solvency crisis (they may have to shut down margin trading altogether), but it should always be able to give customers their assets back. Unless they are misusing customer assets for other things.
They first said they did (we're not insolvent, we're illiquid) but that's already fraud. Then turns out they were also insolvent, as suspected.