Depends on the structure of the PE deal.
There are a few primary strategies. In the most benign situation, a PE actually INTENDS to run the privately-held business well and make its upside from an IPO or a SPAC. This is what happened to my company, and our (former) PE recently finished cashing out all of its stock. And the PE made a tidy bundle.
In the middle-zone, a PE loads up a company with debt, thus taking a first-dollar priority as to (what would have been) the profits. This is the "leverage" model, where interest is "just another expense", though the IRS has made things harder with the interest expense limitation (pain in the *** to compute for the tax people). This is one of those that can test the greed of the PE, as some debt is fine and can be serviced out of the profits, but if the PE pushes the debt lever too hard, it will hobble the company.
In the most extreme situation (like what we just saw with Red Lobster), a PE will asset-strip a company. In the Red Lobster situation, Golden Gate Capital "bought" Red Lobster from Darden for $2.1 million, and then paid for it by selling the underlying real estate for $1.5 billion. This deal destroyed Red Lobster's credit rating and suddenly injected the company with rent expense that it never had previously (and was above-market, which might have worked before COVID, but absolutely is NOT working post-COVID). Sale-leasebacks can work in controlled situations. Shortly after completing construction, WalMart usually sells each store's real estate to an equity investor, BUT WITH A ROCK-SOLID LEASE IN PLACE, one that favors WalMart. That did not happen with Red Lobster.
From what I understand of the college PE deals, it will likely be a DEBT financing, giving the PE a priority on the revenue side, so it's like the second example above. I made a joke to another poster (who is a finance guy) about the schools needing to make a "full-faith-and-credit" pledge (it was a back-handed joke about US government deficit-spending), and he pointed out that the PEs will have first claim to the money. True. But THEN, the money that schools ordinarily received will be double-dinged by both the terms of the NCAA settlement AND any PE money that they accept and have to repay out of revenue. So, long story short, you might see schools having to finance SOME sports expenses out of the general operating fund. We can argue that the money comes from different silos, but money is fungible, so...somebody somewhere eventually pays the price.
And it will probably be the students.