How can it track a phone that’s shut off and not radiating?
You’d have to run out of battery or pull it. When you shut a phone off it still pings. They’re really just in a screen sleep mode.
Some "burner" phones never truly shut off. They reduce the rate at which they ping the cell phone towers in order to save battery life.
Put one inside a faraday cage with an RF monitor and watch how often that phone "lights up". It will be every 10-30 minutes when that phone is supposedly turned off.
Yes, that feature was designed into the phones at the requirement of various governments, so the phones could be tracked. The phone carriers are fully cooperative with such programs and will supply call logs and tracking logs on request to authorized government agencies.
Think of a cell phone as a government-sponsored personal tracking device with a 90-day memory and you have a reasonable assessment of what you are carrying.
The only way to be sure a phone is inactive is to pull the battery from the unit.