They might not have insurance or don't want you to file a claim on their insurance. Any claim you make would impact their premium. Although I don't know the specifics of your accident, if they're responsible for any damage to you (property or bodily injury), their insurance can be held liable. However, it really depends on what coverage they have. If you know their car insurance provider, you can call their claims department and start a claim. In this case, the only coverage that would apply in Illinois
is medical and funeral expenses, which is optional coverage. If they have this coverage, you might be able to get a settlement.