Professors do not buy into an equity in “the firm.” They do not own part of the university, do not vote on their own bonuses, and certainly wouldn’t have the right to dissolve the business (university) or have personal liability for the wrongdoings of the university. I don’t see them like equity partners at all.
If the are at a public university, they may be state employees with the same restrictions as other state employees. When our state passed new restrictions on state employees accepting gifts, they had to check to make sure it would still be okay for university employees, including professors, to accept education benefits, including state scholarships for their children.