Normally if you are driving another person's vehicle the insurance from the owner of the vehicle is primary while your insurance as the driver is secondary or excess and only used after the vehicle's insurance limits have been reached.
If the owner of the vehicle did not have insurance on the vehicle, thus it is an uninsured car, then it should not be driven on the road in most states. In many states if the vehicle is not insured by the registered owner then the registration will be suspended and thus the car is not valid to be on the road.
Now if you were driving an uninsured vehicle and were in an accident, it would be up to your states' laws, your insurance company guidelines and the terms of your policy if your insurance would be extended to the accident damages. It may be that your liability insurance would be available to those that you damaged but that your physical damages coverages of collision or comprehensive would not extend to the person's car that you were driving. Or because there was no primary coverage on the vehicle it may be that your insurance company will not extend any of your coverages to an accident that took place with this vehicle.
To find out if any of your coverages would transfer to a vehicle that you had an accident in and the car was without coverage on it, check with your insurance agent.
If you have a friend or relative that needs to place insurance on their vehicle, have them come here for a quick car insurance quote.