Some libertarians are ignorant of the ability of a group of people to hold private property, jointly. The citizens of a nation are analogous to the shareholders of a company, and they hold the territory as real estate property. That is why they can rightly police the perimeter and control inflows and outflows across the border.

That is why libertarian rhetoric is so often schizophrenic, professing to promote private property, while also promoting open borders (the dissolution of property rights for the citizenry).

Whether we send people home is a decision for the property owners (the citizenry) and they have responded clearly, whenever polled: expell the criminal or destructive, deter additional uninvited immigration, put the economic needs of the citizenry first.

Trespassing is usually a misdemeanor. I think they should have to plea to it, as a matter of justice. They should have to publicly admit that they broke the law, and make restution to the wronged (the citizenry). If they don't want to do that, it shows recalcitrance or even malice, and is cause for banishment. Agreeing to submit to the law of the land should be a prerequisite for their subsequent application for residency. I am against blanket amnesties, as they undermine the rule of law. But I am also against blanket deportation, as they are a hysterical, overwrought reaction, give the federal government too much power, and set a dangerous precedent (it's not only foreigners who can be banished).