It's perfectly possible for funds to return the capital to investors and just say "Hey, we couldn't find anything to invest in at a good price, so we didn't", and that'll look better for them because their ROI will still be good.
This is also likely to happen because big investors generally have their investments split between lots of asset classes by some ratio, so let's say for the sake of argument that Harvard's endowment is 30% equities, 30% private equity, 10% fixed income, and a mix of other stuff. If the value of their equities in the stock market fall through the floor that means their ratio is suddenly off, so they're going to need to rotate out of private equity and into equities.
If I'm understanding you correctly, a capital call is a commitment to provide the capital if the VC firm requests it. I thought it was also a commitment on the part of the VC firm to find investments.
So VCs will have smaller Capital Calls until the market picks up again.
I suspect some VCs will get greedy as their Carry is tied to the amount invested, but the smart ones will play the long game.
This is also likely to happen because big investors generally have their investments split between lots of asset classes by some ratio, so let's say for the sake of argument that Harvard's endowment is 30% equities, 30% private equity, 10% fixed income, and a mix of other stuff. If the value of their equities in the stock market fall through the floor that means their ratio is suddenly off, so they're going to need to rotate out of private equity and into equities.