compromised software - that is the key.
If they decide they want to use your phone as a bug, I wouldn't be too surprised if they could root your phone or change the firmware so that when you push "off" it gives you all of the usual "off" sounds and screens and goes blank... except.
It has to still be active in some way for it to know when you press "on," after all.
It's not like any phones have an actual physical off switch that literally physically opens a circuit. A sliding switch that goes "click?" I haven't seen one of those.