The fundamental error made by the bordertarians (closed-border libertarians) is considering the jurisdictional claims made by criminal cabals which style themselves “states” to be legitimate. From this error comes another, namely that these illegitimately claimed territories in some way become the communal property of the victims (as ranked in an inscrutable hierarchy known only to the ‘enlightened’ bordertarian) of the aforementioned criminal cabals.
The problems with both the premise and the conclusion are numerous, but perhaps the most obvious is that the state never obtained legitimate ownership of the land in question according to libertarian ethics—which require either homesteading unowned land or voluntary trade of legitimately owned land. The bulk of the state’s claims are based on drawing lines on maps and sending armed men (hired with stolen money) to defend the lines. That’s not sufficient to establish ownership. The minority of the land which was arguably purchased was obtained through theft, fraud, and coercion. In other words, none of the state’s claims are legitimate, therefore the state has no authority to allow or disallow access to or use of the land which it does not legitimately own.