Yes, you can get insurance after an accident, but it will not apply retroactively to cover the accident. You will be personally liable for damages resulting from that accident if you were at fault for it. If you do not have sufficient assets, this can seriously jeopardize your finances, and you may face penalties if you do not meet the minimum insurance requirements in your state. Getting auto insurance is critical even if you believe that you are a safe driver and will not cause an accident.