If your car insurance has run out and you're in an accident, get the contact and insurance information of the other driver, since their insurance should cover your expenses if they're at fault. You will almost always be held personally accountable for any damages if your insurance has lapsed and you are partially or entirely at fault in an accident. When the reason for an accident is unknown, police officers and insurance companies are more likely to point the finger at an uninsured driver. Therefore, do not forget to renew your auto insurance on time!
The information in this answer is general in nature and is not legal or insurance advice for your specific situation. Policy language varies carrier by carrier; your declarations page is the final word. If you're unsure, call your agent before you need to file.