- The sponsor gifts the department enough to sustain a faculty member, often salary + research funds, indefinitely (i.e., capital such that the interest pays the bills)
- The department 'names' the professorship
That's it.
But I think the usual corruption risks apply in either case. In the scenario you describe, it's not clear why a commercial sponsor would be motivated to do such a deal. The only direct rewards for the sponsor would be "ad space" in the department name and maybe some sort of reputational bonus for "funding science". But I don't see why a brand like Taco Bell would benefit from either one, especially if the needed investment is massive.
Also, even if there are no obvious conditions to the deal, this always risks inducing some degree of self-censorship on the side of the institution: Someone at the institution will think about what they can do to be attractive for more deals like this - and they'll probably be less welcoming for research that might drive away potential future sponsors.
These profs still have to get funds to get grad students or lab space, and still have to teach to maintain certain benefits. In later years, the endowed chair is essentially a chair in the closet as their research and teaching activity tapers off before retirement.
My spouse was an education-institution major gift fundraiser, so she dealt with endowed professorships, eternal grad student fellowhips, recurring scholarships, and the like. Generally, you can attach as many or as little strings to the gift as you want, but for most things there's no way to enforce those strings after the gift is made and the financial engine starts producing.
Faced with inflation, and the requirement that there is money coming out every X months, I believe it's hard for any other outcome to be achieved.
It's not hard. With an investment of 10,000 you can put it in a high yield savings account and get a few % / year, akin to 100/y. So A million is 10,000 / y. That's a very nice fellowhip "for free" just from a large donation. These aren't actual numbers, they're just a proof of existence of perpetual money from a one-time investment.
inb4 inflation: reduce the yearly outlay by enough to reinvest so the yearly fellowship matches inflation. Your investment just needs to grow faster than inflation.
According to [1] for $5M UCLA will create a new full time professor post. Glassdoor claims the average UCLA professor's salary is $200k so their endowment investments would have to achieve 4% above inflation just to cover the salary. And of course there are a bunch of expenses on top of just salary so you might want more like 6%.
Can an investor reliably get 6% above inflation? In the 1970s no, in the 1990s yes.
Of course nothing is truly eternal - if there were major political upheaval in the United States, a new regime would have 53.2 billion reasons to find Harvard insufficiently loyal.