Does a licensed driver without a car that live in the same household have to be insured under parents policy?

If you drive your parents car then you are required to be scheduled on your parents policy. Failure to do so would be considered insurance fraud by concealment of a known risk. Such concealment can relieve the insurer of any liabilities should an accident or other loss occur while the concealed driver is operating the vehicle, this means they can deny the claim.

All auto insurance policy contracts do require disclosure of all drivers in the household whether licensed or not. All household drivers must be either scheduled for coverage by name or excluded from coverage by name. If you choose to exclude the driver then no coverage is afforded to that driver under any circumstances if an accident or other loss occurs. They are basically driving uninsured and subject personally to all the liabilities, accompanying fines and penalties of any uninsured driver.

That being said, No, There is no legal requirement of law that all insureds in a household be covered under the same policy nor even the same insurance company, but all drivers must have proof of financial responsibility when operating a motor vehicle on public roads.