There's a demand for illegal aliens; consequently, a black market has developed to assist the illegal alien market. I'm simply stating basic Econ 101. You can see it working in now with both parties assisting the black market in illegal aliens by refusing to enforce the laws.
The black market in illegal aliens will lessen somewhat when illegal aliens are forced to follow the rules and wait in line and become legal, according to whatever rules are established and enforced by congress.
Governments, even totalitarian ones, have never succeeded in shutting down black markets. It's just a fact of supply and demand economics.
If there's a demand for something, there will always be a market for it. The fact it may be illegal just increases the attraction of the forbidden good. That's what we have with drugs and prostitution.