The 10th amendment says: "The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people."
How is that relevant to this discussion?
Also, "any hiring is presumed to be 'at will'; that is, the employer is free to discharge individuals 'for good cause, or bad cause, or no cause at all,' and the employee is equally free to quit, strike, or otherwise cease work." speaks only to the relationship between employee and employer. It does not address the eligibility for assistance by any agency.