You will ultimately need to check with the insurer of your commercial truck to see if there will be any coverage from them regarding the accident that a party that was unlicensed and not on the policy was in. Insurance guidelines, as well as policy terms, differ so your insurance provider will be able to tell you what coverages may or may not extend to this situation.
If the driver frequently operated the truck the insurance company may question why he or she was not placed on the policy and may not extend coverage to them. Also the terms of your policy may have exclusion if a person without a valid license drives the vehicle and is in an accident. Check your policy for such exclusions and contact your insurance company to get a definite answer about if this accident that the unlicensed driver was involved in will be covered by your policy.
If there is no coverage on the vehicle and the driver of your truck was at fault, you will need to find out about the liability laws of your state. Likely both the driver and you, the owners of the truck, may be held responsible for damages and injuries he caused.
The driver of the truck should get insurance so that he or she is not longer driving as an uninsured motorist. They can get an affordable car insurance quote by clicking here.