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My Moto X Play on Android 6.0 would automatically power off when the battery displays 2% remaining. When I try to turn it back on, I would get a "low battery" symbol, which means my phone didn't exactly run out of battery yet.
Why does this happen?
Additionally, how can this behaviour be overridden? (say in the event of an emergency and I need to use every last bit of the phone's power?)
Prowler answers your first question well: "Why does this happen" -> Prevents data corruption.
To answer your question "How can this behavior be overridden?"
You can try:
setprop status.battery.level 50 from a shell terminal.
Note that bypassing the shutdown is 10x more risky than a battery pull. However, in a true emergency, benefit > risk.
Why it's more risky:
Battery pull = power loss to logic board, only unsaved data or partial writes / data-locks can cause corruption.
Dry-discharging battery = undervolting entire logic board, 3.0 volts instead of 3.7 volts can be like running your car on 8.5 volts instead of 12: Canbus stops responding, voltage leaks into serial connections, capacitors explode, etc. The same can happen inside your phone, except it's that RAM doesn't hold its correct value, processor misinterprets, accidentally writes the wrong NAND cells, etc, more so after hooking the phone w/ trashed battery up to a charger. The voltage difference between live power and undervolt battery can cause the same leakage onto the I2C bus. (Ever use a car charger with aux cord hooked up to the stereo... The alternator feedback is considered a "safe" amount of leakage onto the I2C bus.)
Why does my phone power off?
It looks like that Android code automatically shuts down when the voltage is 3.4V , battery is 0% . See this answer
Purpose of shutdown as in this answer and also clarified here
This is intended to make sure applications save any required information to disk that is specific to shutting down to prevent loss of user information.
Why does it show low battery symbol indicating phone hasn't run out of battery yet?
Battery status is not real time and probably would take some time to show the actual status
We contacted Google about this, and the indication is that the battery data given in the Settings is the correct one. The updating of the icon happens "every so often", we're told; quite how often is entirely up to the manufacturer, rather than being part of the Android code
Further voltage is NOT a true indicator of the amount of charge. Li Ion batteries display a "flattish" voltage drop even though the amount of charge falls relatively steep as seen here at Fig.2
How can this behavior be overridden?
For versions earlier than 4.2, disabling auto shut down is possible per this DisableCriticalBatteryShutdown. I have not tried this nor do I intend ever trying it, since I always try to charge my battery once it drops to 20% for reasons that become clear on reading Table 2
IMHO, it is an awful idea to let the battery drain to such levels firstly and even worse to attempt to squeeze last drops of juice from it. I would rather recommend in investing in a power bank, if this is a frequent requirement with you
If power bank is not an option, you could use an automation app like MacroDroid to sound an alarm at desired voltage levels, say at 15% (uploaded macro accessible from main menu has a macro for doing exactly this). On alarm sounding, disable services/ apps not required to prolong battery life. In Marshmallow according to Compatibility Definition Document quoted here should give you a complete view of app and hardware power usage
It is not healthy for it to wait until 2%. It should auto power down at around 5%. It is a feature designed to help prevent hardware damage and data corruption. There is no way to over ride it unless somehow, you changed the core code of the OS.
Edit: There is a way to do it without recoding the OS. My bad.
