In case the meaning of the title is unclear, when I speak of "one of the United States", I am using the phrase in its original grammatical and political meaning, which is to refer to one of the individual states that make up the union. Meaning, in other words, one of the United States' states, which the latter is a rather unwieldy construction.

So then, the question is, if the Federal Government wished to abolish, conjoin, or separate one of the 50 states that currently make up the Union, how would they go about doing so? Creating new states is something that there is constitutional and statutory precedent for, with the statutory explanation predating the constitutional, since the Northwest Ordnance, dated to 1787, predates the United States Constitution, dating to 1789. But there is, (I would have to think) no laws detailing how a state can be dissolved, because it is constitutionally forbidden. Article IV, Section 3 states:

New States may be admitted by the Congress into this Union; but no new States shall be formed or erected within the Jurisdiction of any other State; nor any State be formed by the Junction of two or more States, or parts of States, without the Consent of the Legislatures of the States concerned as well as of the Congress.
Meaning that the United States' powers are specifically forbidden to disestablish (or, dare I saw, defenestrate) a state, without that state's consent. I am not sure what the general status of laws within states about dissolution or conjoinment is, either than Texas has its famous Voltron provision to separate into five states, due to historical reasons.

It is not outside of the scope of historical possibility to imagine a time when citizens of other states and of the country as a whole may wish to dissolve a state. It has been an issue for some, from time to time, that the senate skews power towards the less populated state. We can imagine some future time when due to some type of environmental catastrophe, North Dakota is inhabited by only a few thousand residents, living a Mad Max like existence, but still are entitled to the same senatorial representation as California, which is dotted with arcologies, and has a population of close to a billion. But according to aforementioned clause, there is nothing that can be done about this.

Other than, of course, by amending the constitution, which would require two-thirds of both houses of the legislature, and three-quarters of the states to endorse by convention or legislative action. This is a fairly daunting barrier, which is why the constitution gets amended very rarely. In this particular case, it would be an even more daunting barrier, since no small state, (or even a state that fears it might become small), would ever vote for this provision to be amended. But theoretically, at some point, it could be amended.

But even at this point, we bump into one of the few parts of the United States constitution that can not be changed, that is specifically prohibited from being amended by the normal process. According to the section of the constitution that deals with amending the constitution (Article V):

and that no State, without its Consent, shall be deprived of its equal Suffrage in the Senate.
If a state was to be abolished, it would most certainly be losing "equal Suffrage in the Senate". It would go from having two senators to zero senators. Of course, it could be argued that it has not had its suffrage diminished, merely its existence nullified, but I think that logic would say that it amounts to the same thing, and that this passage therefore means that the constitution absolutely forbids, with no provision for amendment, the possibility of the the Federal government abolishing a state.

So the short answer to the titular question is that no State could be abolished under the United States' constitution, unless it wished to be.

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