I think you are missing my point.What is the reason that most petty thieves aren`t up to bloodshed?
How much of it is due to the severity of the punishment that goes along with it.
I am postulating that within the system that you are presenting,which is no government or "official" laws that go with it,that deterrent would possibly be removed.
There already exists areas where there is limited enforcement or respect of laws or the teaching to do so.It is in the inner city and in third world countries.
The absence of government and laws for some reason does not lead to a self restraining individual government or to the communal sharing that Marx envisioned.
How much of it is due to the severity of the punishment that goes along with it.
Very little would be my guess. For the same reason some soldiers freeze in combat and some first time hunters can't pull the trigger.
And no. The Deterrent becomes DEATH at the hands of your intended victim or having to pay direct restitution. Much worse than todays "maybe go to jail".