If the faculty opens a business, there is a conflict of interest, because there is a possibility of the university resources being diverted in to the business. I am going to ask a stupid question. That's an important question. Let's tackle it later, after we finish the issue at hand. Continuing with that, yes you can be involved, can have stock, but cannot be an operating officer.
Full disclosure is the best protection.
When engineering and medical faculty start company, we hide this stuff. We are going to be accused of subterfuge. We have few engineering staff employed full time by the university so that they cannot channel work elsewhere. This is all based on trust and honor because they still supervise students, manage labs. No university has a problem if a faculty ember take's a year's leave of absence.