Power Shutoff to Arduino on Low Battery

I want to power an arduino using the DFR0559, 3.7V battery and solar panel. I see that the device has over-discharge protection to avoid over discharging the battery. When this occurs, will the device cut power to the arduino? This is something I want to happen, but I see in your documentation that the USB port never turns off. Won't this continue to discharge the battery? How can I arrange things so that the arduino shuts down when the protection voltage is reached and then re-boots when the battery reaches the resume charge level?