In situations where you owe more than what the car is worth, the amount still due to your lien holder after they receive the settlement check is your responsibility.

When you owe more than the current value of your vehicle this is called being up-side down on your loan. Your settlement from the insurance company is what they have determined to be the actual cash value (ACV) of your totaled vehicle. This is basically the value of your vehicle in the condition it was before the accident. 

In many states if you are financing a car and owe more than what the car is worth, which happens often since the value of a vehicle goes down as the car is driven off the lot and becomes "used", you can obtain GAP insurance.

With GAP insurance after primary insurance has paid out for a totaled vehicle's ACV, GAP pays the difference between that insurance settlement amount and the loan balance. So this insurance fills in the gap between the settlement amount and the loan amount still due. Without this insurance if there is a balance due on your loan after your insurance settlement then you must continue to pay until the lien holder is paid the full amount of your loan.