This circuit has (as far as I can tell), 0 off current, and 17mA on current. It is latched by the momentary push button, and can be turned off by applying >0.7V at the input as shown. It is intended for use with embedded interactive installation (e.g. an arduino) where the user pushes the button to turn the device on, and the device will turn itself off after some time to conserve battery.
It is a modified version of this circuit.