As long as there are people willing to hire them, they will keep coming. Like drugs, it's the demand that sustains the market.
That may be the simplified version, yet it goes much deeper than that. I don't think home owners or business owners actively search for illegals to do their work for cheaper wages.
A labor need exists, and affordable help is hard to find. When I was a kid, I was lucky to get $5 for cutting a yard. Today, the kids in my neighborhood want $25 to cut the same size yard. You do math, if an illegal came to your house and offered to cut it for $10, would you refuse?
It's even more prevalent in my line of work. I work within the construction industry, and have worked on projects primarily located throughout the Southwest. Many of the workers are Mexican nationals. In the construction industry as a whole, most of them come here for the work, NOT the government handouts.
Most of these guys are more than happy to work at a wage lower than most American workers would accept (which is usually too high to begin with). I don't think this particular group is here to bleed us dry. They risk a lot in travelling to this country looking for work.
And no....I'm not a feel good lefty, I just happen to see a problem that we are continually faced with....and the nationals are a convient (and reliable)answer. It doesn't make it right, but it's not going away either.