He's out-of-status, so if he leaves the country he may face a period of exclusion. You are unwilling or unable to seek to adjust his status on the basis of marriage. That limits his options. He was here on a business travel visa, so presumably he is capable of working. He should consult an immigration lawyer.

Your housing subsidy may be affected by your household income, if you aren't reporting income he's bringing into your household. But that has nothing to do with his qualification to immigrate.