It is not usually state law that requires you to maintain full coverage (liability and physical damage coverages of collision and comprehensive) but the lien holder that will require these coverages.

Your loan or lease documents should state what insurance you are mandated to cover by the financing company while you are paying off the vehicle. This is due to the car being the lien holder's asset or collateral until you pay off the car in full and get title to it.

If you do not obtain and keep full coverage auto insurance on the car, and the lender requires it, then your loan paperwork likely tells what the penalty would be. It may be that the lender will acquire "forced" insurance for the car and bill you for it, which usually costs much more than full coverage but gives you personally less coverage, or they may be able to repossess the car.

It appears that you are from Delaware. The DE Department of Insurance notes that optional coverages of collision, comprehensive, etc are not required by law in Delaware. However, if you take out an auto loan, your bank or lender will likely require collision and comprehensive coverage.

The DE DOI also notes that if you lease a car, you still need auto insurance. You must carry the minimum requirements for the state and the auto dealer or bank will also likely require collision and comprehensive coverage.

You may also be offered – or required – to purchase “gap” insurance. Gap insurance would cover you if you have an accident, the car you are leasing [or have a loan on] is totaled and there is a difference between the amount that you still owe on your lease and the amount you receive from your insurance company after you make a claim. Many leases will include gap insurance as part of your monthly lease payment.