That could happen, but it would affect all LPs equally. If proof of such a call ever leaked the fund would be open to lawsuits from a whole pack of hyenas (high net worth individuals for whom the LP commitment is roughly equal to a scratch lottery ticket to an ordinary citizen) and who collectively represent the larger part of the funds' total commitment.
The people running these funds are not idiots and would not willingly put themselves into a position like that.
Also, if credibly alleged there won't be a next installment of that particular fund.
Such as opening the small talk a Zoom call by saying ‘it’s been a very difficult month for us.’
There are very few VCs who won’t be influenced by a signal even as simple as this one.