Switch off external power on power down?

To fully power down I would like to break the external power supply connection (relay, or mosfet latch) as the last act in shutting down. A control pin would have to be toggled, I suppose that would be off the UI expansion chip.

Ideally there would be only a Power On Pushbutton, with power only removable by system shutdown.

Is there a predefined connection for such…

I have one box scheme with a permanently installed rechargeable battery.