UNITED STATES OF AMERICA :
THE ANSWER IS YES.
I think we should include a bit about what the citizenship laws were at the time our ancestors applied for citizenship, which might vary by state, and how they perhaps changed while in process. This can add some understanding to the history they lived through and the attitudes that prevailed about immigrants, ethnicity, and gender.
You might be surprised at how long it took.
After the American Revolution, people might have not needed a Visa to enter the colonies, but simply have been sworn in after spending a number of years, which might be seven years or more, in which they proved themselves to be self-supporting and good neighbors (rather than criminal).
The general term for this is "One Paper" naturalization.
Prior to that, if one lived in a state that was ruled by Great Britain, then they might have declared their citizenship as British - though they came from Germany. (And then they would, though having come from Germany and had a German surname, give up allegiance to the British King or Queen, rather than a German one.)
Recall that Great Immigration period caused by the Industrial Revolution, at the end of the 19th and beginning of the 20th century, in which people moved from agricultural work to factories. For some time there was a process which started with "First Papers" called "Declaration of Intent." The Declaration in itself had to be updated if there was a change of address or more children were born, or if someone died. The process had to be kept up with, as it was considered suspicious if more than seven years went by and there was no further contact. "Final Papers" are the NATURALIZATION ("Citizenship") papers.
Perhaps because they were Italian - or another "suspicious" ethnicity, an immigrant's citizenship applications were frozen because of World War I. You'll notice it's well after that war before the processing for them continues.
For some time it was only the Head of Household who could apply, implied is a husband, and when he got the citizenship it was for the whole family, his wife and children who were not yet adults. A widowed head of household could apply for herself and her children.
And then there were the women who would loose their citizenship if they married a man who was not a citizen. (I consider that one particularly draconian!)
Women got the vote. And with that came the right and responsibility for adult women to apply for their own citizenship. But check by state because, for instance, women were allowed to vote in Wyoming in 1869, and Utah in 1870 for elections that were not national.
Try on this less thought of scenario. Your ancestor came to the United States and was DEPORTED.
Yes it happened.
Or this one: THEY GAVE UP THEIR U.S. CITIZENSHIP BUT CHANGED THEIR MIND, and had to be REPATRIATED.
On the next couple posts I'm going to refer you to some web sites where you can find out more!
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