If they can’t be, they are not under jurisdiction. Like someone who is a diplomat cannot be arrested and tried in the United States, because they are not under jurisdiction.
But if they CAN be tried and arrested, then they ARE under jurisdiction.
That’s what jurisdiction means.
If this is was the case then you would lose your citizenship ever time you left the United States for a foreign country.
“The fundamental principle of the common law with regard to English nationality was birth within the allegiance, also called “ligealty,” “obedience,” “faith,” or “power” of the King. The principle embraced all persons born within the King’s allegiance and subject to his protection. Such allegiance and protection were mutual — as expressed in the maxim protectio trahit subjectionem, et subjectio protectionem — and were not restricted to natural-born subjects and naturalized subjects, or to those who had taken an oath of allegiance, but were predicable of aliens in amity so long as they were within the kingdom. Children, born in England, of such aliens were therefore natural-born subjects. But the children, born within the realm, of foreign ambassadors, or the children of alien enemies, born during and within their hostile occupation of part of the King’s dominions, were not natural-born subjects because not born within the allegiance, the obedience, or the power, or, as would be said at this day, within the jurisdiction, of the King.”
Why did they say “in amity” - “friendship; peaceful harmony”? If someone enters my house illegally, without my permission, are they in peaceful harmony with me?
When Rome sent people into England illegally in the 1500s, with the intent to overthrow Queen Elizabeth, were they in amity and under the jurisdiction of the Queen?
Ligaility suggests someone “owing primary allegiance and service to a feudal lord”. Do illegal aliens owe primary allegiance and service to the USA? Can we draft them?
Are their children born in “obedience” to the King - or, in the case of the USA, to the Republic? How can they be in obedience if they are here in disobedience?
“Faith” suggests “the obligation of loyalty or fidelity”. Does someone here illegally have the obligation of loyalty and fidelity to the USA?
In what sense, then, is someone born here to an illegal alien born to someone who meets the tests spelled out by the Supreme Court for being “under the jurisdiction”?