Whilst reading a list of minor (compared to the big two) US parties, I noticed there's an Alaskan Independence Party.
Given that the US bought Alaska from Russia, would they legally be free to leave, or is Alaska property?
First, the case of Alaska is far from exceptional. Many states are in territories bought from other states, conquered from other states (which, if you think of it, is just other kind of deal), exchanged for the lives of their previous rulers or just expropiated from their native inhabitants.
The important fact is that the people in these territories organized themselves as states and asked for admission in the USA. From this point on, all of those states were equal to any other state of the USA.
At some point in its history, there was some kind of debate(1) in the USA about whether the states could leave the USA after they had joined it, and the people who said that it was not possible finally convinced the other people. Since then, there have been no changes to the USA Constitution addressing the issue, so that decision stands.
So no, Alaska cannot buy itself from the USA because it is not for sale, Spain has no repurchase option for the Southwest, Mexico cannot claim that the war was unfair, and even if you replace all the people in North Dakota with Native Americans they cannot decide to leave the union.
To further illustrate the point, this video, even when refering to Texas (which at least was an independent entity for ten years), applies to Alaska (as explained above).
Of course, all that is about the current political situation. Make a large part of the population (and I do not mean just 50%) seriously compromised (as in refusing to pay taxes, join the military or the police, etc.) for a time long enough and the political pressure might cause changes to be made to the laws to allow for secession. But success is far from granted and it would be a long and hard struggle.
1 I heard they went to the sea and had a bonfire in a city, so I guess it was some kind of vacation.
Power comes from the barrel of a gun. And the will to use it.
In this case, if Alaska as a state chose to leave, are there people with guns (and other tools) willing to stop them? Will they convince, force, or kill everyone who disagrees, or enough to make it a moot point? If so, Alaska will not have left.
Laws and Constitutions are worth the paper they are written on, and the hearts of those who defend them.
Presuming we play within the laws and constitution of the USA: Under Texas v White the US supreme court held that unilateral secession from the USA was not legal under US law or the constitution.
However, the US constitution can be amended. It is a long, drawn-out process. Adding a means of secession that is clear could be done, thereby nullifying Texas v White.
The process invented by modifying the constitution, or that some secessionists use to convince the USA that they should be allowed to go, may or may not involve repaying the money spent on buying Alaska from Russia.
The question of the right to secession has been conclusively resolved in 1865, and distils down to "NO" .
A bit longer legal analysis is at https://www.alaskabar.org/servlet/content/secession__another_dream_dashed_by_the_court.html
Well, in point of fact, the US did not buy Alaska from Russia. They gave Russia a cheque for a specious claim and threatened Britain to secede its claim just a few months prior to Canadian Confederation. The cheque did not buy the land. To be clear, it was a gift to Russia in exchange for a political justification to a land claim.
The Brits gave up rights when the US pressed a claim which was not valid. If the US had not arranged a bogus purchase then Alaska would have been a part of Canada and a new war would have resulted if the US pushed a claim after confederation.
That said, Alaska is now undeniably a state of the US, just as Hawaii is. The issue of independence is not about money. People in Alaska and Hawaii want more local autonomy just as the provinces of Alberta, BC, and Quebec do. As a Canadian living in Alberta, I'm of the opinion that the structure of politics and autonomy in Canada needs to change.
I suspect many of the people of Alaska and Hawaii think in the same way. Unfortunately I don't see how they can press their claim without personal cost.
The short answer is no, Alaska nor any other state (with the possible exception of Texas) has any right to secede from the United States. This was settled both legally and effectively by the Civil War.
From a practical stand point Alaska can't leave the union. There are simply not enough people or resources to make it happen. Bluntly, even if another country tried to absorb or annex Alaska, even if there was a popular referendum from Alaskans passed unanimously, no country, at this time, has either the economic or military power to make that annexation stick. It's not a fight that anyone is willing to pick and with the amount of military assets stationed there, not to mention the natural resources, there is no way that the US would let them even try.