...for "eavesdropping via their mobile phones even when turned off"

TV series routinely claim that it's possible for law enforcement (=anyone, basically) to switch on a phone that is off.

Nobody has yet made a sufficiently solid case to me that this is possible without physical access to the device. If it's a smartphone, I might buy it (e.g. using bluetooth or wifi to send the phone instructions) but an ordinary handset?

Can someone explain?