The Expatriation Act of 1868 states the right of expatriation is a natural and inherent right of all people” and “that any declaration, instruction, opinion, order, or decision of any officers of this government which restricts, impairs, or questions the right of expatriation, is hereby declared inconsistent with the fundamental principles of this government”.
All United States citizens can become stateless, as long as they are outside the United States when renouncing.
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From the U.S. Department of State Foreign Affairs Manual Volume 7 which reads:
7 FAM 1215 STATELESSNESS RESULTING FROM LOSS OF NATIONALITY (CT:CON-262; 08-06-2008)
a. Persons who renounce their U.S. citizenship or commit any statutory act of expatriation intending thereby to relinquish such citizenship should understand that, unless they already possess a foreign nationality or are assured of acquiring another nationality shortly after completing their renunciation, they will become stateless and severe hardship to them could result. In the absence of a second nationality, those individuals U.S. Department of State Foreign Affairs Manual Volume 7―Consular Affairs would become stateless. Even if they possess permanent resident status in a foreign country, they could encounter difficulties continuing to reside there without a nationality.
b. The U.S. Government generally cannot accord stateless former U.S. nationals the consular assistance that is provided for U.S. citizens and U.S. noncitizen nationals pursuant to the Vienna Convention on Consular Relations (VCCR), U.S. statutes and regulations, and customary international law.
c. Stateless former U.S. nationals may also find it difficult or impossible to travel as they may not be issued a U.S. passport, and would probably not be able to obtain a passport or any other travel document from any country. Further, a person who has renounced U.S. citizenship will be required to apply for a visa to travel to the United States, just as other aliens do. If found ineligible for a visa, he or she could be permanently barred from the United States.
d. Expatriation will not necessarily prevent a former citizen's deportation from a foreign country to the United States, nor will it necessarily exempt that person from being prosecuted in the United States for any outstanding criminal charges or held liable for any military obligations or any taxes owed to the United States. The fact that a person has been rendered stateless does not serve to nullify the individual’s expatriation if the renunciation is done voluntarily and with the intention to relinquish U.S. nationality.
e. In making all these points clear to potentially stateless renunciants, the Department of State will, nevertheless, afford them their right to expatriate. We will accept and approve renunciations of persons who do not already possess another nationality. It should be noted, however, that if a foreign state deports such individuals, he or she may find themselves deported to the United States, the country of their former nationality.
You can find the full text of the State Department Manual Here.