About the business use of an employee's auto, from an insurance perspective
A lot of employees use their personal vehicles on company time. I'm not only talking about driving from home to work and back, but also business meetings or driving between the companies' headquarters.
The most common policy offered by insurance carriers to meet such needs is the so-called "business auto policy". It works for all business purposes, except for "livery", defined as carrying goods or people in exchange for a fee.
The driver's insurance policy will always act as primary in case of an accident, regardless of the circumstances and the purpose with which the car was driven. In other words, even if you drive the car during work time, your insurance will kick in if you have an accident.
A standard business auto policy does not protect the employee in case of a lawsuit, so individual drivers will need their own insurance for such cases. The main purpose of the business policy is to protect the employer, and not the driver.
Most businesses will not bother to get anything on top of liability insurance for non-owned cars. Protecting the employee's car is not their responsibility, not to mention that the additional costs would be unjustifiable. Most employees who drive cars under this kind of protection already have their own comprehensive or collision policies and, as I mentioned above, these are primary in case of an accident. So even if the business was to buy extra coverage, it would only be effective if the employee's policy didn't cover enough.
An example should illustrate the concepts better. Assume John drives his personal car and does an errand for his employer, ABC Ltd. John has a Liability umbrella policy of $300,000, and ABC has a business auto policy for non-owned cars with $1,000,000 limits. John doesn't have comprehensive or collision coverage. He causes an accident resulting in $5,000 damages to his car, $25,000 damage to others' property and $600,000 in hospital bills for injured passengers. John will be personally liable for fixing his car, because it's an uncovered incident. His insurance company will pay $25,000 in property damages and $275,000 in medical expenses, and ABC's policy will provide the remaining $325,000.