You can always purchase insurance after a car accident, but it will not cover a past accident. It will only apply to future accidents. Even if you buy insurance the next day, it will not help you in an accident that has already occurred.   The penalty for driving without liability coverage varies by state. A car accident lawyer can guide you in a case like this.   If you are found to be at fault for the accident, you’ll have to pay for the damage out of pocket. You could also be sued by other people for damages.   If you were not at fault, state laws may still limit what kind of expenses you can recoup.