Your loan company typically would find out about your change in auto insurance because they will require you list them as an additional insured and the lien holder of the car with your insurance carrier. Thus the insurance company may notify them of changes with the auto insurance policy that could affect the lien holder's asset, the car.

For your own knowledge, an Additional Insured is a person or an organization, other than the named insured or covered person, who is protected under the named insured's auto policy. If an auto is leased, the leasing company may want to be listed as an Additional Insured as well as a lien holder or loss payee. This protects the leasing company if it's named in a lawsuit for an accident caused by a policyholder.

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.

Your loan company may also have the right to repossess your vehicle if you to not keep the required "full coverage" they require on it.

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 is any that specifically apply to your situation, you may try contacting the consumer division of your state's insurance regulator.