As I am licensed in Florida and Vermont, I cannot comment specifically on Illinois state law. However, generally, a mere cosigner on the loan, but not a titled owner on the vehicle, is usually not liable for injuries caused by another driver. However, under certain factual circumstances, that may not be true. If the cosigner provided money or secured the vehicle for the driver by cosigning and this cosigner knew that the person who would be driving the vehicle presented an unreasonable risk to the public (for example, was a known drunk, addicted to drugs, had a horrible driving record, was an epileptic prone to uncontrollable seizures etc.) then there may be liability on the cosigner for enabling or negligently entrusting this vehicle to the driver. We had a case such as this in the state of Vermont a number of years ago, where a grandmother facilitated the purchase of a vehicle for her grandson, who she knew to be an unqualified driver. The grandmother was found responsible and ordered to pay the damages caused by her grandson.
The co-signed would not be liable for damages under the facts you stated. Your queston indicates that the driver of the vehicle, although possibly uninsured, was not at fault in the accident. If the driver was not liable for the accident, there is no way the co-signer could be liable for the accident. The only way the co-signer would be liable for damages is if he negligently entrusted a vehicle in which he owned to someone he knew of should of know would use the vehicle recklessly. Proving negligent entrustment in IL is difficult unless the driver of the vehicle had prior moving violations, had displayed reckless driving in the past, or was under the influence and the co-signer knew or should have known. Failure to carry insurance, while against the law, doesn't not make one liable for an accident. If the hit and run driver was totally at fault, the passenger can't claim that the driver was negligent. That said, the co-signer may be in trouble with the lender if the vehicle was uninsured and the loan was secured by the vehicle. Most loan agreements obligate the borrowers to keep the vehicle (the collateral) insured. If the borrowers fail to do so, the lender may repossess the vehicle, may place collateral insurance on the vehicle and charge the borrowers, or, if the uninsured vehicle is destroyed, the lender can demand full payment of the balance of the loan. If the driver doesn't pay, the lender will come after the co-signer.
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