In some states everyone has workers comp by default through a state uninsured employers fund. If a business owner fails to buy insurance, workers comp still covers losses, but the business owner has to pay penalties and could be subject to jail time and so on. Also the workers comp statutes in some states only protect the direct employer, not a client of the employer, from a lawsuit. So the workers comp system actually functions to limit claims by employees against employers. If you are not the employer, then someone else's employees may have claims against you. Workers comp will not cover those unless you are able to qualify as an employer by definition. That could happen if you work with a temp agency for example.
So in short the failure of a business you hire to obtain workers comp could be a problem in some states. In general, you are only indirectly affected by it because you are choosing to hire a company that probably cuts corners.