This is not about US Citizenship but about being a citizen of a specific US state. US citizens living overseas can apparently lose their state citizenship and this may restrict some of their legal rights. Desperate but, presumably, the lawyers think it could work
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Citizen of a State
The Fourteenth Amendment provides that American citizens are also citizens "of the state wherein they reside," but U.S. citizenship does not necessitate residence in a particular state.
Persons living abroad, for example, are citizens of the United States but not of any state.
One significant legal disadvantage exists for a person who is not a citizen of a state. The Constitution provides that federal courts can hear "Controversies … between Citizens of different States." The phrase "Citizens of different States" includes citizens of Puerto Rico, the Virgin Islands of the United States, and Guam. Puerto Rico is in the First Circuit, the Virgin Islands are in the Third Circuit, and Guam, Alaska, and Hawaii are in the Ninth Circuit. A person who is not a resident of a state or designated area, even if he or she is a U.S. citizen, cannot satisfy the diversity of citizenship requirement and therefore cannot bring an action under the Diversity Clause in a federal court.
Definition of Citizen of a State in the Legal Dictionary by The Free Dictionary
legal-dictionary.thefreedictionary.com