The standard auto policy excludes coverage for non-owned vehicles furnished or available for your regular use. This means you are relying solely on the company's insurance for protection. If for any reason the company's policy does not respond if you are in a traffic accident, you have no coverage.
The company's business auto coverage will also not provide you protection if you use the vehicle outside the scope of the employer's permission. This can leave a big gap if you or a family member use the vehicle in a way that wasn't part of the original agreement.
Your company gave you permission to use the car, but you are the only one allowed to drive it. Your spouse takes the company car to the grocery store and on the way she crashes into another vehicle.
Unfortunately, you have no coverage on either your policy or the company's policy. In other words, you would be on the hook for damage to the vehicle and possibly the other vehicle, as well as for medical costs for any injuries sustained by either party in the accident.
If you are given a company car, you should consider adding an "extended non-owned coverage for named individuals" endorsement to your policy. You should name each member of your family of driving age.
This endorsement will fix the gap in coverage when an employee is furnished an auto for their regular use (or even has one available for their regular use out of a pool of vehicles). But, note that this is only for liability coverage and there is not going to be any physical damage coverage for the vehicle.
This endorsement is inexpensive and can provide peace of mind. It is a good idea anytime you have regular access to a vehicle you do not own.
If the insurance company won't add the extended non-owned endorsement (or a similar one) to the personal auto policy, or can't add it, the next option would be to buy a named non-owned policy to fill the gap in coverage. In effect, this accomplishes the same thing as the extended non-owned coverage for a named individual, but may be more expensive.