It is uncertain what you mean by "driver's insurance". There is a kind of liability insurance called "non-owners coverage" that is often required under a state's Financial Responsibility Law when an individual has been in an at-fault collision, did not have the required liability coverage and when the other party's damages exceeded a stated amount, or when an injury occurs. It is also sometimes required when a judgment is entered against an individual for an auto collision and the judgment remains unsatisfied. Non-owners coverage generally will "follow the driver" irrespective of the vehicle that he or she is driving. Non-owners coverage provides no coverage for the vehicle itself such as for its repair or replacement in the event of a collision.
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