How come things like mp3 players and flashlights can go down to 0 battery and aren't damaged?
It depends on what you mean by
"0 battery"... &
how you know they haven't been damaged?
If you mean
0%, they most probably are governed by a BMS that deactivate further use of the battery to protect it... but if you let it lay around without charging it there, it will eventually self-discharge below the lowest cell voltage & there it's goodbye, the flashlight/MP3 player will not turn on anymore & will not take charge.
You also need to understand that most of the ordinary household gadgets which have smaller Lithium cells aren't required to provide similar high amp draw as for our drones, which can go up to around 20A for a photo drone & even up to 70-100A for racing quads. If a flashlight battery is worn & fails it will not be catastrophic... it will just not turn on anymore, not fall as a rock from 400ft.
Also, most smaller gadgets use Li-Ion batteries (usually cylindrical shaped) & that chemistry have it's lowest limit at 2,5V/cell... instead of 3V for a LiPo... this will give a Li-Ion a bit more headroom before getting permanently damaged, but once low enough they will also stop working.
Have had at least 2 remote controllers (with squarish LiPo cells) for my TV that have suffered from swelling batteries to a degree that I couldn't get them out of the remote anymore. Both of these remotes had a stand which charged them... & obviously the remote was always placed there every evening, so the batteries was never really discharged, instead fully charged all the time.
And as said earlier... a BMS in a DJI battery indicate 0% when the cell voltage is 3,5V, that's a good enough cut-off limit where no major damage occurs.
But after 3,5V the voltage drops very fast to damaging levels... that's why you shouldn't fly your batteries down to 0%