"Supervising" may be overstating the case. Collaborations, of course, can be valuable if a faculty person is interested in applications of theory to real world problems. The same collaborations can be valuable to industry if theoretical expertise is needed and not present in the company. Papers arising out of such collaborations can be as valuable as any other.
Some industry folk work in the other direction, coming to the university to collaborate on things of mutual interest.
The collaborations I've done haven't been paid, but resulted in fairly informal grants that I could use for travel and other research support. Some (not all) of the (industry) people I worked with were doctoral students at the university and their research was peripherally related to the project, though not directly. It was a learning experience all around. One of the projects I was involved with resulted in a major change of direction in an important segment of the company. They were, in fact, seeking solutions to important problems from academics. A couple of us were able to provide that assistance.
Side hustles, such as a separate business (an accounting professor working for an accounting firm, say), are possible and do happen, but most universities will control them in some way, often by forbidding them for full time faculty. They may be more important in those places where faculty salary is very low.