Squint enough and you'll see a cellphone consists of two primary chipsets: a main SOC/stack that runs the operating system, and a modem/software stack that pushes cell packets. Power the phone down and you (may) fully shut down the OS/processor; you likely aren't powering down the modem.

Some phones when turned off would power on every ~10-15 minutes or so to check for text messages, which effectively pings cell phone towers.

I doubt they can if it's it dead, but as long as it has some charge the chips in your phone can use it without any indication to you.