Car insurance is written to cover a specific vehicle, not a specific driver. If you do not have a car to insure, purchasing a car insurance policy would be pointless. On the other hand, many vehicles are owned by dealerships or organizations and driven by people who have possession of the car but do not own it.
Technically, any car that you are not making payments on is not your car, and some circumstances, such as leasing the vehicle, involve your use of a car that you will never own outright. Since most states require any vehicle operated on public roads to be insured, insurance companies are required to offer non-owner liability coverage which meets or exceeds the state minimum requirements.
To be sure, non-owner car insurance is a minimum level of insurance. You may also need to purchase additional riders or coverages, such as uninsured/underinsured insurance, and dealerships may also require you to carry GAP insurance which pays off the vehicle if it is totaled in an accident or stolen. Comprehensive coverage includes vandalism and burglary, and is not part of the standard non-owner package but may be purchased separately to protect yourself against such malicious acts.