The common assumption amongst most in New York is likely that it is impossible to "accidently" commit a crime (particularly a federal one). Thus, claims if innocence to criminal activity are often met with great deal of skepticism. However, there are indeed where circumstances unbeknownst to you could indeed invite criminal scrutiny, especially if you are in the business of employing the others.
For example, you may have not been aware of the fact that employing an illegal alien is indeed a federal crime. Sure enough, Section 1908 of the U.S. Attorney's Criminal Resource Manual states that it is illegal to hire an unauthorized alien or to continue to employ one whose immigration status (at least with respect to his or her employment) had changed. Furthermore, you cannot refer employees (for a finder's fee) to other companies if those employees are in the U.S. illegally. Doing so could make you subject to significant fines and penalties.
Those penalties may be compounded even further if it is determined that you engaged in a "pattern of practice" in violating this statute. Say who hired three employees who turned out to be unauthorized aliens. You could be made to pay a fine of $3000 for each one, or face a six-month term of imprisonment for each employee (or a combination of both).
To qualify to be charged under this statute, however, it would have to be shown that you hired said employees knowing of their immigration status. If the fact that they were here illegally was withheld from you, you cannot be held accountable. In fact, the federal offense would then shift to the individual employee if he or she used false documents (or misused valid ones) in order to verify his or her eligibility for employment.