It sounds like prior to joining your company he may have been in financial hardship, so that rather than use his new salary to start renting a place immediately

It sounds like prior to joining your company he may have been in financial hardship, so that rather than use his new salary to start renting a place immediately, he would rather pay down debt and build up savings. Or he might have not gotten around to or not know how to go about finding a place. In either case, you should talk to him about it. If his reasons are financial, you might find out that he has a timeline in mind (eg 'after my student loan is paid' or 'when I have $x savings'). You might consider offering a salary increase to offset the rent. If it's about getting around to apartment-hunting, you can pay a real estate agent to book him apartment showings. It's probably important for him to have a decent psychiatrist. He may be defensive about that; I'd go into that conversation with a non-threatening narrative in mind.