A certain sound plays when your tools run out of durability, but this sound also applies to zombies and skeletons. If you kill a mob that spawned with armor, the breaking sound plays, unless the mob drops all of its armor. This does not apply to held items (like a zobie wielding a sword).
How to Reproduce
#Spam zombie or skeleton spawn eggs until you get a mob with armor. You can also find a mob in the wild.
#Kill the mob that spawned with armor.
#Listen to the sound that the mob makes when it dies.
The mob should only make its normal death sound.
If the mob does not drop all of its armor, its normal death sound plays (as expected), but so does the armor breaking sound.