If I were tasked to implement this, I would arrange for the phone to appear to be powered down when in fact is is not, and for malware to do this when shutting down from inside the normal OS. If you "powered off" from software (by shutting down from a menu or holding the power down until the screen goes blank, but not the many seconds it takes to trigger a more hardware-level hard power off), then I would make the screen go blank and make all other inputs unresponsive, except for the normal power on input.

For bonus points, I would arrange for the baseband to transmit only very minimally as necessary, so it isn't noisily detectable from RF pickups such as nearby speakers.

The technical details would get simplified, and management would hear that I can track a "powered-down" phone.