Can an employer hire illegal immigrants?

Employers face very, very serious consequences for knowingly hiring undocumented foreign nationals or foreign nationals who do not have valid work authorization. You can talk to your employer about these issues or the Department of Labor.

Not without very severe consequences. Talk to an experienced employment immigration lawyer to get additional advice.

employer holds risky responsibility

If you want to take some action (such as reporting this illegal activity to someone within the company or to DHS), you should first probably get some advice from an employment lawyer. Although it would be unlawful for your employer to fire you for reporting unlawful hiring practices, it does happen. You may also be subject to some form of retaliation short of termination. Furthermore, although it would be unlawful for your employer to retaliate against you as long as you had a good faith belief that unlawful conduct was occurring, it's much better to be right than to have to use the good faith argument. Talk to an employment lawyer; explain your position in the company, the extent of the unlawful hiring, the reasons you are convinced false documents are being used, and the company's likely response before you proceed.