The fact that an employee is categorized as "contract" or receives a 1099 does not necessarily answer the question of whether they are covered under workers' compensation. These situations are decided on a case by case basis and depend on the amount of control the employer has over the worker. It's best to consult with an attorney before jumping to a conclusion. In Illinois, employers are required to be insured, even if they have just one part-time employee. There are exceptions, of course. And members of an LLC can exempt themselves.
That is the million dollar question. The IRS and courts have been wrestling with what the definition of an "employee" versus an "independent contractor" is for years. It depends and I would suggest you consult with a lawyer specializing in workers' compensation coverage issues.