>>65068
You'd likely get something akin to the Cospaian Elder Council, Icelandic Goddard, Somali Xeer, Colonial-years Pennsylvanian township, etc. E.G. The government doesn't exist except on paper, or if it does exist, it has no actual power in practice. Something that can make a press release to the media but doesn't have the power to really do anything that people haven't explicitly agreed to.
That or it might come down to a series of legal battles within the state itself. The state would likely not want to start a full-blown conflict since those tend to be counterproductive with the advent of the modern firearm (and fully automatic firearms would be far cheaper in AnCapistan since the only thing keeping gun prices high/stopping anyone from owning a full auto rifle now is the ATF in 'Murica 3-burst is best burst though.). So with that in mind, it would probably go to a legal court inside the state's system in which a few scenarios could happen:
The State could relinquish their claim or have the judge relinquish the state's claim over it, setting a precedent.
The State could insist on their claim until violence broke out at which point they'd be fighting a propaganda war since they technically invaded.
The State could sign a deal with the landowner to fork over the property for monetary compensation or something to a similar effect, driving up the value of the rest of AnCapistani lands still left/preventing further encroachment (since the lack of regulations would mean the AnCapistanis would be worth more than FiatDollar #XYZ).
In all cases of compromise (assuming the home owner didn't just whip out their raifu and tell the state to fuck off), you end up reaching a point of equilibrium where the state lacks an incentive to push further for more land as they'll be met with greater resistance. Simply put the state has to be stupider than normal to do so.