In a hit-and-run accident where the at-fault driver runs and never gets caught, the damages they caused will be covered by the injured driver’s own auto insurance company. This type of coverage in hit-and-run accidents falls under the “uninsured motorist” section of the auto insurance policy. Your insurance company covers all the damages and if the suspect driver is ever identified down the road, the insurance company will go after his or her insurance for reimbursement.