FICA (Social Security and Medicare tax) are levied on dollar 1 ($1). So, your employer is treating you as either an independent contractor or "under the table).
There are IRS regulations regarding employee versus independent contractor. Many construction companies try to classify their employees as contractors.
The reason an employer does this is to avoid payroll taxes. An employer has to contribute to FICA for each employee, pay unemployment tax (state and federal) and carry worker's compensation insurance. By treating employees as contractors, they believe they can avoid these expenses.
You can contact the IRS, your state's Department of Taxation/Revenue (for state withholding) and your state's unemployment commission to report this employer. They will be happy to do an audit and determine if the employer is falsifying records or not.