Let's say that a generation ship sent into space by NASA returns to Earth many years in the future, and find that the United States is a relic of the past. The land that used to be the U.S. is split up into pieces that belong to a bunch of different countries, so it's not even like you can say there is one country that all former U.S. citizens became a part of. So now this ship of people who are technically U.S. citizens (having been born on a space ship that is U.S. property) lands on Earth. How would they be dealt with? Can any country legally claim these people as their own citizens? Who would have authority over them?
closed as off-topic by AndreiROM, TrEs-2b, Green, Hohmannfan, cobaltduck Oct 13 '16 at 18:49
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If your country is gone and you go to another one, you are basically a refugee from your home country. The country you go to then has the self-given right to add you as a citizen, deport you, or imprison you. Largely depends on what their government is like.
There is also the part of how do they land? While in space, Maritime law is in effect, so no country has legal jurisdiction on them until they land. (Of course, language barriers would still be a problem.)
EDIT: (adding notes from comments)
While in space, you can do whatever you want (other people also reserve the right to shoot you if they don't like you though, though that might attract bad attention without good reason). Once you land, the country you land in determines how to process you, and what you are allowed to do (as you no longer have your old country to seek embassy with).
Also, if different people land in different countries, each country has jurisdiction only on the people who landed in their territory. Since they aren't legal citizens though, if they flee the country, that country has no jurisdiction to pursue them (and the country they flee into will gain jurisdiction over them).
And for completeness (thanks Molot), assuming that your home nation just split/reformed/was taken over, than you may still be a citizen depending on the rules they made (if the new countries still honor them). (see Citizenship of Russia about when the Soviet Union ended. Particularly the Citizenship acts) In that case, you have all the pros/cons of already being a citizen of a country.
I would think that the citizens and their ship would then become the USA (should probably rename themselves to simply "America") in orbit (a generation ship would be WAY too big to land).
Now, the UN or whatever passes for that in the future may or may not recognize your giant spaceship in the sky as a country. There wouldn't be much need for trade, as a gen-ship is self sustaining, so unless, your "Americans" decide to retake all or part of North America, you'd be pretty much fine in orbit.