If what you are saying is true, and he was given a 1099, then the company was doing something illegal and he would be in his rights to report them. The report would be taken very seriously because if true the company is committing tax fraud.
I'm not sure how that would be tax fraud. The company pays the guy, that guy reports his income to the government, and he gets taxed on the income he reported. If he chooses not to report his income, that would be his own problem, not the company's problem.
The company must report his pay to the IRS, either with a 1099 or a W2.
I think it would just get reported as a business expense, similar to calling a plumber to fix the toilet. The contractor would need to give an invoice, and the company would use that invoice to get the tax deduction. It's assumed the contractor would report that invoice as his income, so he would be the one paying taxes on it. If that contractor happens to be Wesley Snipes, he won't pay tax on it, and he'll get sent to prison for a while.
Now that I think about it, I'm not really sure why it would be illegal for a company to pay people under the table. Without any invoice or pay stub to prove that someone was paid, that money would appear on the company's balance sheet as profit, so the company would need to pay tax on that money. The employee would not pay income tax on that money, but the employer would, so the money gets taxed regardless or how it changed hands.
edit: Mentioning the words
balance sheet made me understand why this is important. The last thing anyone wants is corporations having inaccurate balance sheets saying they have X amount of profit but that money doesn't really exist because it was paid out to undocumented employees. We had a lot of financial reforms after 1929 so companies have very strict guidelines when it comes to financial reporting.