All of the State’s money and assets originate in theft, so the best it can do, even theoretically, is return exactly what it stole. But it's restitution debt is necessarily greater than that.
The desirability of a state's fiat currency depends on the state making future threats of violence against tax payers - in particular coercing them to pay taxes denominated in the local fiat currency. So fiat is an inappropriate restitution remedy in this context.
If the victim population was unanimously opposed to allowing entry to members of group X, the most just border policy a state could impose would be to exclude members of group X.
Imagine a thief steals money from people A, B, and C and uses it to build a farm. The thief somehow remains the nominal owner of the farm. The farm is the only possession of value the thief has. [ctd]
It's clearly better from a libertarian/restitutive stand point if A, B, and C have exclusive use and management of the farm than if the thief allows everyone to use it and aggressively prohibits A, B, and C from excluding others from using what is rightfully theirs.
If victims' summed preferences, weighted by the severity of the states' restitution debt to each individual, lean more towards 'exclude group X' than they do towards 'allow group X', the more just route is to have the state exclude X.
Both open and closed border policies, when implemented by a state, involve the violation of peoples rights. The question of which is least unjust in any given case is an empirical one that can't easily be settled.
A policy that excludes group X violates the rights of the owners of developed public property who would want people from that group to have use of the property.
A policy that fails to exclude group X means that the state is providing less restitution than it could do, to the owners of developed public property who want group X excluded from the property. i.e. It's committing a more severe degree of rights violation.
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