Can you collect from both insurance companies from yesterday's car accident the old insurance coverage will expire today?

As a Broker, AND this actually happening to me just last year, I can FOR SURE tell you YES. As long as your policy was still in effect until midnight of the expiry date, you are covered. eg. I had accident on July 2, and it was to be ceased on July 3rd. No joke! Talk about ironic and a piss-off to my insurer!