What Apple should tell you when you lose your iPhone
Find My IPhone should allow the owner of a stolen phone to make it so that the phone cannot be turned off by the power switch on the device itself.   For non-4G/non-LTE devices, It should also aggressively look for open access points and attempt to associate with them and phone home to Apple servers with location info.  Activating stolen mode should also put the phone into a power conservation mode to keep it alive and phoning home as long as possible.