State laws can vary as well as the terms of a loan or lease can differ from one financial institution to another. It is possible that the finance company can require you to carry full coverage on the vehicle in the name of the person on the loan. If this is stipulated in the loan documents and you carry the required insurance but are excluded, it may not be enough to meet the finance company's requirements.

When a lien holder finds that the insurance they mandate is not on their asset, the car, the way in which they require it to be then likely the financial paperwork states that they can place "forced" insurance on the car.

The lien holder normally has a right to protect their interest or collateral, the vehicle, by getting "forced" insurance on it if they find that you do not have insurance or it or do not have insurance that meets their documented requirements. If your loan agreement includes the provision allowing the lien holder to obtain auto insurance for the vehicle, the insurance charges are subject to interest in most states so the premiums will be much higher than if you purchased the insurance yourself typically.

To find out what your finance company is allowed to do, read through your loan documents. Beyond that, to find out about insurance laws in your state and if there are any that specifically apply to your situation, you may try contacting the consumer division of your state's insurance regulator.