I know tenured professors who don't apply for grants, and therefore don't have any money to pay students, but they still get paid a salary by the department. They can do whatever they want (research, or not), modulo teaching responsibilities. Some profs actually do very good research, without students. It's a reasonable way to go, once you have tenure.
Problem is, you can't take that route to get tenure in the first place, unless you're an absolute genius.
Most places are redefining tenure though, so the only people that still have any meaningful resources are those that have extramural funding. Anymore, tenure means you get a closet for an office and a phone. And for new hires, if you don't have grant support, even with tenure, you can still lose your job.
Problem is, you can't take that route to get tenure in the first place, unless you're an absolute genius.