Yes, indeed an important and difficult question! It's really like asking what happens in a forest where nobody is around to see it?
You would have to start with a fundamental analysis of the assets to calculate its key risk factors, and then find one or more liquid indices as a reference. For example, if you have a portfolio private credit instruments, you should calculate their duration, convexity, etc., but also their sectors and implied ratings based on some basic credit metrics. Then you can match it to benchmark bonds with similar credit risk.
Then you should consider that there is an added liquid risk. If you're buying them at +100 bp to liquid assets, just be careful that in a bad market, there could be no bids for the illiquid assets, or it could be +500 or +1000 bp to liquid benchmark assets. (Yes, seriously, that much worse.)
This doesn't mean that they should be marked down as much, but you should have enough liquidity cushion to ride out those markets.