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.