Ponzi schemes are an extreme example, because the fund is illiquid because it lied about its investments and simply stole the funds, meaning there's absolutely no way to cover.
But there's a lot of ways this can occur. This basically describes a "bank run"; you nominally have an agreement you can withdraw your cash at any time, but if everybody does it at once there's a problem because the bank is using it to do things like fund mortgages, which can not simply be called back in instantly if needed. Even if the bank has the right to do that, and for various things it sometimes does (taking "financial instrument" generally and not just "US mortgage"), it would still be squeezing blood from a stone; they can demand it but it doesn't mean they'll get it.
In recent news, Blackrock suspended withdrawing from a UK real estate fund, because investors have been withdrawing at a rate that would require them to liquidate their holdings at fire sale rates, further depressing the fund's value: https://uk.finance.yahoo.com/news/blackrock-halts-withdrawal... Same sort of thing. No "Ponzi" scheme here; there's some legitimate financial stress, but that stress would only be exacerbated by letting everyone withdraw. (Whether you agree that it is justified to halt withdrawals in this case or not, I'm just using it as an example of the generality of this structure.)
I can't pull it up quickly in a news article because I'm not coming up with the right search terms to pull it out of the noise of constant financial news, but when Janet Yellen was Treasury Secretary, she had floated a trial balloon about trying to fix this incentive problem with bank runs against real banks with the same sort of clawback scheme, the idea being to disincentivize a bank run in the first place by making it so you don't get the pattern where the first few people get all their stuff and everybody else loses everything, which is a huge contributor to the run occurring in the first place. The game theory on this one gets a bit complicated if you think about it. e.g., OK, if everybody else is going to sit tight because this scheme incentivizes them to stay in the bank, then it's safe for me to withdraw everything because the bank run was prevented in the first place. If they then hold things together "long enough", then I can say I did it for my own reasons, not the bank run that was delayed for six months while everyone else sat tight, before an ultimate collapse. But if everybody thinks that way... etc. Not clear to me whether this can actually prevent bank runs, which I mean straight, not as a weak sarcastic "no this obviously wouldn't work". Not clear. Complicated analysis.
This structure is not intrinsically morally wrong or anything. It's a basic tool, and you need some kind of structure to bridge between high liquidity and low liquidity like that, and such a thing will intrinsically have some "impedance mismatch" to it, to use a favorite technical metaphor. But it does have a certain amount of risk intrinsic to it that can be a bit difficult to characterize; the problem is that a given instance of it failing is likely to be highly correlated with a lot of other instances of it failing at the same time. Naive analysis of the risk is utterly inadequate, and being sophisticated and correct about it is easier said than done.