Earlier quoted context omitted.
Complete speculation here, but I wouldn't be surprised if devices could keep broadcasting the ping after they're "dead". Tiles last for years without charging, so I bet if Apple can leave on only the bluetooth beacon after the battery drains past where it can power the rest of the phone then this would be doable. Again complete speculation, I have zero clue if the current hardware is even capable of doing this.
The current hardware might not be, but you could run this on a secondary chip similar in specs to the T2 or Secure Enclave. You could theoretically even have a second battery specifically for this purpose, but that would likely be cost-prohibitive.
They could probably use a cut down derivative of the W2 chip used in AirPods with the audio codec etc. removed. I’m guessing phone batteries reach a point where they’re still storing energy but can’t provide enough current to safely boot the whole phone. The BLE chip could sip on the remainder of the battery for a long time.