Note that freed-market anarchism is just one end of the more broader free-market left libertarian spectrum, which does not intrinsically preclude governments and law enforcement.
With that in mind, consider what would happen today if you were to claim some random empty house as your own, posted a sign to that effect outside, and started to shoot any "trespassers". That would be murder - and the law would come down on you. Same thing would happen in this hypothetical society if someone tried to do what you describe.
(The issue of how a fully anarchist society would deal with murder in the first place is a separate and complicated one. I can't really speak for them; my own take is that anarchism is a kind of political asymptote - an unachievable utopia that the realistically-possible ideal society would trend towards as its cultural underpinnings evolve to make it more viable. In this day and age, something like Bookchin's libertarian municipalism appears to be empirically viable.)
With that in mind, consider what would happen today if you were to claim some random empty house as your own, posted a sign to that effect outside, and started to shoot any "trespassers". That would be murder - and the law would come down on you. Same thing would happen in this hypothetical society if someone tried to do what you describe.
(The issue of how a fully anarchist society would deal with murder in the first place is a separate and complicated one. I can't really speak for them; my own take is that anarchism is a kind of political asymptote - an unachievable utopia that the realistically-possible ideal society would trend towards as its cultural underpinnings evolve to make it more viable. In this day and age, something like Bookchin's libertarian municipalism appears to be empirically viable.)