Illegal aliens cannot get green cards because they are illegal aliens.
Green cards must be applied for in their home country and they have to wait their turn there.
Well, then that is more argument to deport them all and bar the illegals from ever becoming legal. Also, companies who are repeat violators should be put out of business and their owners put in prison for a very long time.
It took about one year of paperwork and waiting in the USA to get a work visa for Japan. I had to prove to the Japanese government that my talents and skills were so specialized that Japanese nationals would not be harmed by my work. Most countries have a similar policy. Also, illegals, if caught working, were treated very harshly. The companies too.