While every driver in Illinois is obliged to have liability insurance, there is a possibility that the person at-fault hasn't followed this regulation as well. In standard cases, the insurance company of the person at-fault could be held accountable for the compensation that you deserve.
However, in cases where the person at fault does not have an insurance policy or the limit is not sufficient, they will be responsible for providing the compensation. This will make the case more complicated, but it can still be pursued.
Another way of going about it is to file an uninsured motorist claim with your insurance company. This way, if the person responsible for the crash doesn't have insurance, or it becomes a hit and run situation; you can still recover your losses through your insurance company.