Who has more decision making power? 1 man with 5 billion dollars, or 6 billion people, each with 1 dollar?
The former, due to both the communication effort required for the 6 billion people to organise themselves and to information asymmetry. If there's some critical information required to make a decision, each of the 6 billion people either has to discover it themselves or trust someone else, and the latter hands power over to those they trust. The man with 5 billion dollars only has to discover it once, and can pay people to assist him which incentivises them to behave in a trustworthy fashion. It's the same reason that the SEC restricts some forms of investments to "accredited investors".
How would this 'death penalty' be enforced without a State?
That's quite simple really. The market would ensure that those unable to support themselves financially would be unable to obtain food and would starve to death. (Of course, in practice this wouldn't work and state intervention would be required, but that's true of the market in general anyway.)
Well, some well-reasoned and logical responses.
In the first instance, you're right, communication does indeed pose a problem, and does even now. However, in the market, when one party is injured, it's not just them that stop dealing with the inuring party. Word of mouth is a pretty powerful force, especially in a small community. The world is getting smaller, and information only has to go through 5 or six hops to get all the way around the world. Imagine what it would be like in an even more connected world. Piss off the wrong people, and you're penniless.
In the second one, What you've described is essentially the enforcement mechanism in an AnCap society. Unemployment would only come to those with truly nothing to offer, and for those few unfortunates, charities, or more likely employers who are willing to train, would take care of them. Shunning, excluding someone from interactions, would only come as a result of failing to enter arbitration. So while death by starvation is possible, it's not likely to come from simple unemployment.