Can my accident be covered if my insurance cancelled the day before the accident but the cancellation letter was received the day after the accident?

This depends upon the date of the cancellation.  If the date of the cancellation was the day before the accident, then your insurance was not in effect at the time of the accident.  Generally, a cancellation notice will give a cancellation date.  It is not generally dependent upon the date you receive the notice.  You can double check by calling your insurance and asking for the official cancellation date. 

In Ca there is a 30 day grace period. Depends what state the accident happened in. Are you pursuing a claim against the other driver or vice versa?