First to all who know This post is for people who don't !
Far as I can tell Illegal immigrants can only arrive via the Star Gate .
So once you build it if you don't want them keep the gate deactivated unless your using it to sell or import ..
I have 0 illegals at 78 k colonists I had over 430 when I deactivated the gate it slowly drooped to 0 so it even works if you already have them .
It solves the Always homeless as you have more colonists then homes .
It solves the always a few sick as you have more colonists then homes .
I stay at 0 sick and 0 homeless and 0 unemployed
From The wall that works