So, I can give you my own experience and some links.
As a battery of a smartphone is dying, it performs a few tasks automatically. Think of it as a creature that's freezing and is trying to preserve energy/life/heat for its most important functions. It differs a little between models, but the basics are:
Low Power Mode reduces the amount of power that your iPhone uses when the battery gets low. It optimizes performance for essential tasks like making and receiving calls, sending and receiving email and messages, and accessing the internet.
support.apple.com
- at 20% to 10%, most phones enter your typical 'low battery' mode. At 20% your phone will ask you if you want to enter low battery. When it drops under 10%-ish, it will do so automatically.
- Low battery mode disables a number of features, depending on the phone. From disabling 3-5G, to shutting down half the cores, it makes less handshakes with towers. That's how I am assuming they knew that the battery was draining leading up to the 10:30ish pm 'the phone ran out of battery'. They did not see the screen shut down; they only know that it stopped handshaking with the tower between 10:30ish pm and 4:30ish am.
HOWEVER.
- When an iPhone dies, it isn’t genuinely empty of battery power. Instead, a small percentage remains to power its wireless chips that can be used with the Find My feature. If you’ve ever lost your iPhone, you know that you can utilize the feature to track its location.
Your iPhone is a lifeline to many daily activities. When it dies, it can cause problems. But here are three things it can still do.
www.komando.com
The phone keeps protecting its vital wireless chips, so IMO it is very likely that it either a) it wasn't fully drained, just on a very low battery mode, and it did one final attempt to connect while it was powering off proper
Or
b) it was powered off, but someone was using 'find my iphone' which forced the wireless chip to reconnect, thus receiving all the messages.
All MOO
(I am no longer in tech, so a lot of this info might be wrong or outdated. It is correct IMO but super happy to hear from more experienced people.)