Payroll

The IRS says you must report all income which includes cash. If you are an illegal immigrant working in the US and you fail to report cash income that is tax evasion. The law says you must get an ITIN and use that to file your taxes. If you are paid by check then the employer withholds taxes including payroll tax. You can file and get a refund on any income tax withheld but you will not get the payroll tax back and these contributions to social security will never provide any retirement benefits to you.