How will we ensure that they stay in Mexico?
Nothing would stop 10 guys all coming to claim they worked illegally using the same stolen Social Security number, also nothing would stop 1 illegal from claiming to have worked with 4 or 5 stolen Social Security numbers -- or establishing 4 or 5 separate identities that each claim to have worked her with stolen or fraudulent identification documents.
I bet there will be very generous payments being made for the "survivors" such as widows and needy offspring of the felony document fraud criminals.