Help: does my medical insurance end on the last day I work in my

 I will leave my current company late August. Due to mover's busy schedule, there is around 1 week gap between my last day in my current company and the new company. Because I have a little son, I worry about our medical insurance.  Does my medical insurance end on the last day I work in my current company? If so, how can I get a cheap insurance for a week or 2 weeks? Thanks a lot!