When you are big enough liquidity and solvency are the same thing.

There's also maybe the option of being insolvent but nobody caring because the money is too good..?

Not sure what to call this since I assume this has been regulated to death in normal finance ?

But it wouldn't surprise me if it had happened at some point at FTX, considering all the greed and hype around crypto...

Though I guess it might be a moot point : information doesn't travel instantly, and a judge might still deem you "guilty of Ponzi" (or whatever term is appropriate) if you haven't literally been shouting "We are insolvent !" from the rooftops ? See again : regulation.

"Trading while insolvent" we call it in the UK; the legal obligation is to call in the administrators when you realize you're insolvent. Which they have now done. And insolvent companies generally do themselves, because it's less painful than the alternative.

There will probably be a lengthy argument in court (but which court - Bahamas?) as to whether they should have realized this earlier and whether their accounting was deceptive or incompetent.

(those interested should read "Lying for Money" by Dan Davies, it's an entertaining and escalating history of fraud)

"Trading while insolvent" is called "equity" or "unsecured loan", and it's legal and regulated.