Are you familiar with the grammatical concept of a substantive noun? It's when an adjective is used as a noun (as with the word "variable", for example). A subject of a government is someone who's subject to its jurisdiction.
That means, by the way, subject to its jurisdiction at all times, even when he's out of the country. That's why a U.S. citizen who engages in child prostitution in Thailand can be prosecuted by U.S. authorities. That's why Johnny Jihad was charged with treason, despite the fact that his actions took place in Afghanistan.
And what made them owe allegiance to the U.S.? Again -- kidnapping? Please, someone, tell me by what legal mechanism first-generation slaves lost their citizenship of their country of birth in Africa.
However grossly immoral it was, it was perfectly legal under our laws at the time. That's just a fact we have to face. And it's really beside the point, because slave imports from Africa were cut off in 1808, so there'd have been nary an American former slave alive in 1868 who'd even know what the country of his ancestors' origin was, or in many cases, who is ancestors were. America is the only country they ever knew.
One does not have to be "subject to the jurisdiction" at all times. You can be subject to the jurisdiction of the country you're temporarily in. Local police can arrest you, you can be prosecuted by local authorities in local courts, and you then go to local prison. That doesn't mean that if you return to your home country, you couldn't also be prosecuted there, if their laws are written that way. You are conflating the two senses of the word "subject", by insisting that "subject to the jurisdiction thereof" incorporates the meaning of "a subject of". Check out Websters 1928 Dictionary for examples of "subject to" -- quite normal and ordinary usage. Just because Bouvier's only defines the noun, doesn't mean that was its only or most frequent usage.
I am not arguing that slaverly wasn't perfectly legal in this country. I am saying that kidnapping someone and transporting them against their will to another country does not automatically strip them of their citizenship, and bestow upon them the citizenship of their "host" country. If that were so, someone kidnapped in Bosnia, or Zambia or Pakistan, and transported to Guantanamo would automatically become an American citizen. Or Cuban, if you prefer. As the Fourteenth Amendment says, if you are born in this country, and you are subject to the jurisdiction of this country (meaning not immune, such as diplomat or child of a diplomat), then you are an American citizen.
There are many people in this country today who don't know the origins of their forefathers, not even if they were legal immigrants or not, and America is the only country they've ever known. (Many immigrants changed their names, and invented new stories for themselves when starting a new life). So are you saying they shouldn't be Americans? Even if their parents were born here? And their parent's parents? If it's just a matter of multiple generations, or passing of time, or ignorance of your origins, how many generations? How much time? How much ignorance?