Accounting for Distress and Illiquidity.

Alerts: Assume an undergraduate understanding in finance and accounting, taught at any average undergrad business major. Also - Beware, a lot of hypotheticals ahead.

I have been going through Damodaran's Valuation playlist on YouTube for a while now. I couldn't wrap my head around two key areas:
a. In one of the sessions, he talks about Distress. He says that a traditional DCF is not equipped to take care of the distressed case. He suggests a few measures to incorporate the distress perspective into a DCF.
b. He also talks about the illiquidity of assets and some basic ways to add it to the valuation numbers.

My problem with his prescribed methods is that I don't understand the workings of a few methods and the math he used for them. For instance - he used probit to come up with the numbers for solving the distress case. I did not know anything about the addon or how it is used. So, I was mostly lost.

Imagine a hypothetical situation - you are building a valuation report to understand the intrinsic value of a small-cap firm. There are no precedent transactions to help you out here (the firm is relatively new or mostly unheard of in the market). How would you take care of the somewhat probable distress case and the illiquidity case?

On a tangential note - do you even have to care about probability of a distressed case if you are creating the very first DCF model of a public company that you may use in the very initial stages of building an investment memo?

Please feel free to paint any broad-stroke ideas or suggest any theoretical material you might have used earlier to understand distressed valuation or quantifying an illiquidity premium.