Hey, take the offered asylum in Mexico or go home! Not welcome in the US.
Most will end up working in Mexico for a year til they can pay a coyotes to take them into the US...... After all even little kids interviewed in Mexican schools boast of their goals to go to the USA when they grow up...and their teachers encourage this.
So they will likely stay awhile but will continue their drive to the US. They know and believe there will be a way into the US.