A human has no natural attacks, so I'll use him, but any humanoid character without damage features works too. No magic. Let's exclude any character class that can earn a damage bonus. Monk, barbarians, etc...
Anyone can do an unarmed melee attack. It deals 1 + STR modifier bludegoning damage.
An unarmed person with STR 7 should do 1 minus 2 damage. Nothing. Even if it is a critical.
Is the person above unable to kill anything in combat without a weapon?
Regarding the concerns about the purpose of the question:
Are you only interested in killing via reduction of HP? I.e. are you looking for ways to kill as an unequipped weakling, or are you looking to confirm your reading of low-STR unarmed strikes? – nitsua60♦
Kill can be achieved by any combat option that does not involve the use of weapons (improvised or otherwise) or environment. Does not have and cannot pickup any object.
- Looking for ways to kill as an unequipped weakling, without class features.