When Jeff Bezos takes all the coconuts and says you can have them if and only if you suck his dick...
So I was discussing property rights and this situation came up. And I had this thought: the billionaire buying the island and forcing the other inhabitant or inhabitants to do certain things they don't consent to, that scenario, is not justified for the same reason that theoretical doughnut homesteads are not justified.
By claiming everything needed for the continued control of the other inhabitants' own bodies, the billionaire has initiated a conflict over the control of their bodies. He thus has committed aggression against them by definition, even if the local law enforcement and every other observer of the trade thinks it's all a legit purchase. A good jurist would recognize this, and an arbitrator applying the natural law correctly, in light of the facts, would identify that this happened and hold the billionaire accountable and let the other inhabitants go free, or otherwise create some resolution that preserves the property rights of everyone involved to the best degree they can and holding the aggressor liable to proportional restitution and retribution, and the victim would have the right to choose how much of a sentence they wish to carry out within the maximum limits.
This sentence could be handed to local police or to a bounty hunter or carried out by the victim himself.