Quadibloc ranted: If there were no police, there would be nothing stopping store owners from taking shoplifters, killing them, and selling the body parts to hospitals. Except public opinon. And since shoplifters are initiators of force, it isn't clear to me that public opinion would necessarily be against this sort of thing in all conceivable AnCap societies - even if it would be strongly against it in some or even most of them.
In an AnCap society, shoplifters would be armed, just as everybody else is. Even if they had little support from public opinion, they'd be able to defend themselves. I'd lay odds that, over time, public opinion would tend toward an idea of appropriate justice, which would rule out killing shoplifters and selling their body parts, but would accept milder forms of abuse, more proportionate to the crime.
More to the point, shoplifting would decline in an AnCap society. There would be less hardship, since no government would be stealing ( taxing ) to support itself; nor would the government be restricting access to markets; people would have many more legitimate ways to put food on the table. The idea of entrepreneurs as faceless "exploiters" would lose popularity, as the government schools and government-supported media disappeared. There might be left a tiny core of people who shoplift not because they need to, but because it is an odd hobby. Those people might enjoy the risk of the occasional duel.
But, by and large, "an armed society is a polite society", and an AnCap society would not restrict ownership of personal weapons. Google "not so wild west" and lay to rest your lurid fantasies of shoplifters being slain for body parts. Observe that, in the ungoverned west, their was greater respect for private property than in the "civilized" East.
From an AnCap perspective, this makes perfect sense. Socialist production of goods and services, including the service of justice and defense of property, is inefficient compared to market production of the same. It is not at all surprising that, in a free market ( AnCap ) society, there would be more peace and justice and security, and less murder or theft, compared to a society encumbered with government efforts to provide security.