I'm concerned that our company is using contingent staffing labor and that not all of the workers are legal. Do we have any responsibility and exposure or is that all the problem of the outsource company?
I don't think you have any liabilities as long as they are your outsource company's employees. As a form of due diligence I would ask what their process is for ensuring they are hiring only those legally eligible to work in the United States. You could also have them sign a document that states that all of their employees are ... (ex: E-verified, background checked...) and to the best of their knowledge all of their employees are legally eligible to work in the United States.