Consider this improbable yet possible scenario (which nonetheless came up at our table last night):
A PC is unconscious and currently making Death Saving Throws. A weak (8 Strength) and hostile NPC tries to punch the PC to kill it for good.
Attack rolls against an Unconscious character have advantage and any attack that hits the character is a Critical Hit if the attacker is within 5 feet of the character
The NPC rolls with advantage and beats the PC's AC. It is therefore a critical hit.
If an Unconscious character takes damage while at 0 HP, they automatically fail one death saving throw, or 2 death saves if the damage is from a critical hit. Massive Damage can still outright kill the character so damage should still be rolled and if it equals or exceeds their max HP then they die
Ok, so that's 2 failed Death Saving Throws for the PC! Let's calculate the damage, just in case…
Instead of using a weapon to make a melee weapon attack, you can use an unarmed strike: a punch, kick, head–butt, or similar forceful blow (none of which count as weapons). On a hit, an unarmed strike deals bludgeoning damage equal to 1 + your Strength modifier. You are proficient with your unarmed strikes.
Here, 1 + STR = 0. The hit deals 0 damage. Does that even count as damage then?
Does the attack actually provoke failed Death Saving Throws?
If so, how many?
Can an unarmed strike even crit if there are no dice being thrown?