Insurance follows the vehicle. The at-fault individual may not have insurance, but perhaps the car he was driving is owned and insured by someone else. This could still be a dead-end if the person that hit you didn't have persmission to use the car or is an excluded driver.
Does your auto insurance policy include collision coverage? Consider filing a claim if the amount of damage exceeds the collision deductible. You owe the deductible even though the crash was not your fault. Subrogation is a process that enables the insurance company to request reimbursement for the claim (including your deductible) from the at-fault driver. You may get back all or a portion of your dedectible based on subrogation results.
If you don't have collision coverage, perhaps your policy has uninsured motorist property damage. UMPD pays for damage to your vehicle caused by an identified, uninsured driver. There is a $20,000 limit and $1,000 deductible.
You can pay repairs out-of-pocket or seek legal counsel if you have a liability-only policy. A liability-only policy pays when the insured individual is legally responsible for another person's crash-related damages. This type of policy provides no coverage for repairs to your owned vehicle.