How does iPhone location update when the phone is turned off?

If you shut off an iPhone, the main Find My mechanism will not be able to report the phone's location.

However, if Find My Network was enabled, the phone may send out periodic Bluetooth beacons even when turned "off". If another Apple device comes close enough and hears one of them, it may report an estimate of the phone's location – in a manner similar to how AirTags work.

Even if you power off the phone, the phone will send out very brief intermittent Bluetooth signals. If another Apple device is in close proximity to the phone, that device can pick up the signal from the iPhone and use that to report information on the iPhone's location.

Now, if the battery has completely run down, the iPhone won't be able to send out any location information.

if it's fully off then it has no functionality whatsoever

but clicking on the normal off button does not turn an iPhone fully off

you need to take extra steps do to do that.

Turn iPhone on or off - Apple Support