I have refused to work someone who was not legal...it is not legal for me to work them. I would not rent to anyone in my home....legal or not. But the illegal part makes it certain.
Your "don't have a spare room" reminded me of the Russian "communal apartments", a subject not related in any way to the subject of this post (up to four pages yet!! But then the whole post is based on conjecture, so why not?).
Those were the days my friend, we thought they'd never end...