What is the ruling of Islamic law on living with a Muslim person who is engaged in an illicit relationship in the home, when it is difficult to find alternative housing?

He who brings his girlfriend to his home has erred, for women are a great trial (fitna). Your duty is to cease living with him if he does not heed your advice, lest you be afflicted by theana and become accustomed to evil. If you are compelled to live with him due to the unavailability of safe housing for your religion, then there is no harm, provided you intend to leave him as soon as you are able, or emigrate if you find no other solution.