There are, of course, requirements for employers to verify the immigration status of all employees before they hire them and employers have been fined and jailed for hiring illegal immigrants (as discussed here). Any kind of suspicion that an employer may be hiring illegal workers can be reported to the U.S. Immigration and Customs Enforcement at the number indicated here.
However, an employee, unless an employee has a written employment contract or a union contract, is normally considered an "employee-at-will," and employers can hire or fire an employee-at-will at any time, for any reason, or for no reason at all (except where there is discrimination or other illegal activity). Discrimination may be said to occur where an employer fires a US citizen to hire non-US citizens (this is an idea, not a proven matter), because discrimination due to national origin is illegal. But, again, that is only a potential legal theory, a possibility.
You may want to consider speaking to an attorney (often, many initial consultations are free), perhaps one who works in employment law, to review your situation to see if you may have any claims against a former employer given your situation.