Every employer in the country should be mandated to run every person they hire through the E-Verify system to ensure the people they are hiring are US citizens or those that are legally allowed to work in the United States.
Also, any payroll processing company that processes a paycheck to a person not legally permitted to work in the US should be held accountable along with the employer.
The current I-9 form verification system is wholly inadequate as those forms are not submitted nor reviewed by any authority.