Legal Question in Personal Injury in Illinois

If the other company is offering you a settlement you are free to reject it. If you accept a settlement and it involves a payment to you and transferring the car to them, then that is the agreement you made.

It's often easier to make a claim to your own insurance and let them sort out the details. If you had liability only, or no insurance, you either negotiate with the other party's insurance, accept their offer, or reject their offer and sue in small claims court (assuming damage is less than $10,000).

You can always negotiate.... Always.

Almost. They are obligated to pay for any repairs NOT EXCEEDING the fair market value (FMV) of your vehicle. If the offer is too low, you can demand a market survey. This may not help if the car is customized. Once the cost of needed repairs exceeds the FMV, they hand you a check and you hand them the title unless you want to buy the car for its salvage value and keep the car.