You can ask them if you can pay the premium to reinstate the policy, but given that it was cancelled on December 2nd, you're probably past that point. Without insurance, you are personally liable for any damage you caused in the accident, to yourself, your own property, as well as anyone else or their property. You'll also likely be cited for driving without insurance if law enforcement is involved - don't fail to report the accident if your state's laws require it, even if you will then get a ticket for not having insurance. The penalty for not reporting an accident will be worse.

Stop driving your car immediately and don't drive it again until you have insurance.

The police arrived at the scene and only gave me a citation since I was the one that rear ended the other car. Their end of the car looked ok as it was main cosmetic. The car seems totaled.

I gave them the policy number that "was" my pervious policy and I am assuming they ran it.

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Yes, it sounds like you’ll be paying for everything out of pocket. Insurance isn’t going to cover anything.

would the lender not have placed any insurance on the car?

Unlikely they’d figure out you were uninsured that quickly, and if they had, they would have told you and charged you. Certainly call and ask, but it’s unlikely.

Have you asked insurance about reinstating the policy and paying back premiums?

Doubtful. It takes them a long time to do this.

You’re probably also going to be in hot water with your lender because they almost certainly require this asset to be insured, which it wasn’t. Don’t stop paying that car note unless you want the lender to come after you with a vengeance.

Insurance is the driver’s responsibility, not the lender’s.