A vehicle, whether it is being used commercially or privately, must be insured by the owner. Commercial insurance policies typically insure company cars and trucks for all licensed drivers, with each one being listed as a driver. If a truck driver then hits a car, the deductible for the claim would be the responsibility of the company or its owner.
In some circumstances, you may liable for the cost of the deductible to the company. If so, this would be spelled in your employment contract with the company, and would require your signature prior to operating the truck. In this situation, the owner of the vehicle is transferring the financial impact of the accident to the person who caused it. The deductible is actually paid by the vehicle owner and then reimbursed by the truck driver.
If Personal Injury Protection insurance is involved, the owner of the car that was hit may have paid their own deductible. In this situation, their insurance company would handle the full claim and then contact the insurance company which covers the truck. Through a process called subrogation, the two insurers then negotiate the settlement of the policy behind the scenes. In the end, the car driver would receive their deductible back from the responsible party.
The truck driver, not the vehicle owner, would receive any points related to the accident on their driving record. In this manner, both the owner of the vehicle and the driver must take responsibility. The owner is responsible for the deductible and insurance, and the driver is penalized for having points on their driving record.