In Louisiana if you do not have liability coverage on your car at the time of an accident, the "No Pay, No Play" law would apply. That is, an individual who does not have liability insurance cannot collect for the first $10,000 of damages in an accident, no matter who is at fault.
Louisiana's "No Pay, No Play" statute (La. Revised Statute 32:866) would apply if you were in a wreck without insurance due to your coverage being cancelled.
This statute which became effective in 1998 forbids a motor vehicle owner who does not have liability insurance from recovering the first ten-thousand dollars of any bodily injury or property damage claim. This means if you are driving a car without insurance you give up the right to collect your first ten-thousand dollars of personal injury and property damage claims.
If you were at fault in the accident then you of course would have no insurance to make a claim through and will likely be held personally responsible for the other party's damages that you caused.
The penalties for driving without insurance in Louisiana if you are cited by LA law enforcement is that the car can be impounded, your registration and license plates (tags) can be suspended or revoked as well being hit with fines and administrative fees.
As for your insurance being cancelled, under ordinary circumstances, after you have had an insurance policy for 60 days in LA, that policy can only be cancelled if you fail to pay your premium, you file a fraudulent claim, or you or a member of your household has a driver's license or motor vehicle registration suspended during the policy period.
If your insurance company decides not to renew your policy, you must be given a 20-day notice, and the company must give you the reason for non-renewal if you request it in writing. So if your insurance was canceled you should have been notified.
If your insurance was canceled without you being notified then you may want to contact the Louisiana Department of Insurance to see what consumer advice they may be able to give you on this subject. Contact the Louisiana DOI at 1-800-259-5300 or 225-342-5900 in Baton Rouge.