I take it you mean, if your car IS repossessed. In that case, IF you dont plan to redeem it, NO. NO car, NO insurance. Once the lender repos the car, they are responsible for the insurance coverage.
If it's no longer your vehicle, you don't need to insure it.
No, you dont even need keys to repossess a car in South Carolina
A creditor can repossess a vehicle at any time after a default(late payment, lack of insurance, etc.) occurs on the contract.
The best insurance for a commercial vehicle is a comprehensive plan that provides not only liability coverage, but also includes coverage for cargo, and the vehicle itself.
Then they will repossess the wrecked vehicle, sell it for what they can get, apply that to the loan balance, and you will be responsible for the balance on the loan. They will sue you in court to get it and will win. Now if you continue to make the loan payments, then none of this will happen. Did you not have insurance on this vehicle?
Of course. The financing agreement that you signed requires you to have full coverage insurance and to make sure that they receive a copy of the insurance with their name listed as leinholder on the policy. This assures that they are paid if there is an accident and that they are notified in case of a cancellation of the insurance. There are laws protecting the leinholder in every state. If you break the contract with the leinholder they have the right to repossess the vehicle as well as the put what is called forced place insurance on the vehicle. This insurance protect the leinholder's interest only in case of an accident or damage to the vehicle. This coverage is physical damage coverage only and does not include liability or any other coverages and the premium is very high. The premium is charged to your loan account.
Your personal auto coverage will not cover their vehicles. What they are probably asking for is to make sure you have coverage in case you drive your vehicle on errands or such for the company. If you go to the post office to get the company mail your personal auto insurance will be the primary insurance and then if they have an endorsement to their insurance called "hired and non-owned auto" it will provide secondary coverage over and above your coverage to protect them in case of an accident. Their coverage insists that you as the employee have primary insurance on your vehicle. Also note that the company insurance will not pay for damage to your vehicle.
In automobile insurance, collision coverage provides for repairing a vehicle when it is damaged due to the fault of the insured. Liability insurance provides for cost of repair of the OTHER vehicle if you damaged it.
Some insurance companies like Progressive will cover a non-owned vehicle meaning a vehicle in which you have no legal or financial interest. Check around if your insurance company does not provide coverage to non-owned vehicles.
Barring any exclusions in the policy, the insurance 'stays with the car' so your insurance will pay for the damage to the innocent persons vehicle (under your liablity coverage). If you have collison coverage on your vehicle/policy it too will pay to repair your vehicle less the deductible. If there is no collision coverage on your vehicle and the driver has a policy with collision coverage the drivers collision coverage may step in and repair your vehicle, but ONLY if you don't have collision coverage.
Usually, it is the responsibility of the owner. However, if you have insurance on your vehicle, they will step in as secondary coverage...including covering the damage to the vehicle you were driving, if you have the coverage.
In this state, a no fault state, full coverage insurance covers the other vehicle if you are at fault.