Unladen liability is used in motor carrier/trucking terminology to refer to liability coverage while a truck is operated with an attached empty trailer that is not hauling cargo (i.e., deadheading) or without any trailer (i.e., bobtailing), regardless of whether the truck is dispatched or not.
This term is often used interchangeably with "bobtail" or "non-trucking liability," but unladen liability has a broader scope since it includes both liability for deadheading or bobtailing regardless of dispatch status.