Have there been any countries that voted themselves out of existence?

There was the case of Carpathian Ruthenia: after Austria-Hungary collapsed in 1918, the region claimed independence, and after some rather complicated back-and-forth between Hungarian Democratic Republic, West Ukrainian People's Republic and Czechoslovakia, a newly formed National Council voted to join Czechoslovakia for a promise of near-autonomy.

However, I'm not sure if this is applicable - the other contenders claiming that it was practically an annexation, with Czechoslovakia holding the area by military force against the Hungarian Soviet Republic.

In a similar vein, ceding the area from Czechoslovakia to USSR in 1945 was officially voluntary, but with the area already effectively under Soviet control.

https://en.wikipedia.org/wiki/Carpathian_Ruthenia#Transitional_period_(1918%E2%80%931919)

Relatively recently there is the Cocos (Keeling) Islands.

Technically they did not vote themselves out of existence but were given the choice of independence vs integration with Australia.

The islands were claimed by the Clunies-Ross family in the early 19th century. In 1857 the islands were annexed by the British Empire. In 1955 the islands were transferred to Australia, note that the Clunies-Ross family still owned the vast majority of the land. Due to their feudal style of ruling, Australia forced the family to sell the islands in 1978. In 1984 the locals voted on their future from 3 choices. Full independence, free association, or integration with Australia. They chose the third option.

American Samoa used to be an independent nation. In 1900 the chiefs got together and gave their country to the United States, an event celebrated every year as Flag Day. When I lived there and worked as editor of the newspaper, I referred to it as Dependence Day in an editorial. This ruffled some feathers, perhaps because it was correct.

The US was interested because the main island, Tutuila, with its capital town of Pago Pago, has a natural deep water harbor with a protecting dogleg that's a great place to park warships during a typhoon. There's also an airport with a runway large enough to land anything. During World War II there were more marines on Tutuila than Samoans. Since joining the US as an unincorporated territory the country has benefited from an inflow of US government cash, along with facilitation of trade with the US. Samoans born there are nationals, but not citizens, of the US.

Scotland and England

By the Acts of Union 1707 the kingdoms of England and Scotland (which were in personal union under Anne) united to form the Kingdom of Great Britain.

Great Britain and Ireland

Similarly, the Acts of Union 1800 merged the Kingdom of Great Britain and the Kingdom of Ireland into the Kingdom of Great Britain and Ireland.

German post-World War II history has two examples of a free democratically elected goverment deciding to give up independence and join another state; in both cases, the state they joined was the Federal Republic of Germany.

The first example is the Saar Protectorate which had been separated from French-occupied Germany in 1947. Its degree of independence was questionable as it was effectively governed from Paris and was required to use French currency but it did get its own consitution, its own government, have its own political parties independent of the French ones and, most visibly for most of the world, participated in international sporting events as Saarland rather than Germany or France (in fact, in the qualification for the 1954 FIFA football world cup, Saarland and (West) Germany played two qualifying matches against each other which the FRG won 6:1 aggregate).

In 1955, a referendum was held whether the Saar Statute should be adopted, effectively increasing Saar independence but retaining the economic union with France. This Statute was rejected by 68 % of voters with a turnout of incredible 97 %. The result was acknowledged by all parties as the will of the Saar population to rejoin Germany – or rather newly join the Federal Republic of Germany. On the 14th December 1956, the parliament of the Saar Region declared its accession to the FRG and on the 23rd December of the same year the Law of Incorporation of the Saar Area (Gesetz zur Eingliederung des Saargebiets) of the FRG came into force declaring the Saar Protectorate as the new 10th German state, the Federal State Saarland.

The second example is the one more commonly known as German reunification: the end of the German Democratic Republic. In brief, after what is known as the Peaceful Revolution of 1989, the first free election in East Germany was held on 18th March 1990. In this election, the CDU and its partners in the Alliance for Germany won 48 % of the vote share (93 % turnout). The subsequent government was a grand coalition encompassing the Alliance for Germany, the East German SPD (social democratic) and the liberals.

All parties in government plus a couple more had campaigned for the accession of East Germany to West Germany and indeed that was the politics they assumed rather rapidly. On 23rd August 1990, the Volkskammer (People’s Chamber, the GDR parliament) declared the accession to West Germany which was effected on the 3rd October.

You may well argue that the Saar case was not exactly a fully independent and sovereign nation although the decision making was fully democratic including a referendum. I don’t see much opposition one could come up with against the East German case where the general election was effectively the referendum.

Since you posit the country remaining in some form as a subnational unit, such examples are actually rather common.

Apart from the examples already given, from modern history see the admission of Baltic states to the USSR (at a gunpoint, but still there was a voting by the new puppet revolutionary parliaments). A bit more voluntary was the accession of Tannu Tuva to the USSR, the Anschluß of Austria to Germany, the annexation of Crimea, the reintegration of Bantustans to South Africa; while the integration of Far Eastern Republic to the USSR has been a mere formality and the annexation of Hawaii was supported by at least the non-indigenous population (the indigenous people did not count).

I am deliberately not mentioning unifications where the parties were at least formally equal (e.g. creation of Yugoslavia, Switzerland, Romania, Bulgaria, Gran Colombia, UAE, UAR etc.)

The Kingdom of Sikkim voted to unite with India, in a referendum in 1975. It was in culmination of the internal strife in the country between the Crown and the pro-democracy Sikkim National Congress.

Wiki

In 1938 Austria had a referendum on becoming part of Germany.

The vote was not democratic as Austria had been occupied by Germany at the time, but it still led to the „Anschluss“ of Austria to Germany.

In 1707, the parliament of the sovereign state that was Scotland (with its own currency, parliament and legal system) voted to join an incorporating Union with England. This led to Scottish MPs going to the Parliament in Westminster.

The vote was highly suspect; Scottish MPS were openly bribed with land and money to vote for the Union. As a result, a country that had resisted English military aggression for centuries, volunteered to surrender its independence. The poet Robert Burns, had this to say:

The English steel we could disdain,
Secure in valour's station;
But English gold has been our bane -
Such a parcel of rogues in a nation!

Another interesting example - though almost the opposite of voting to join another country - is Czechoslovakia, which voted to divide itself into two countries, Slovakia and the Czech Republic: https://en.wikipedia.org/wiki/Czechoslovakia

You could also include the reunification of Germany, or the various states of the Italian peninsula deciding to become a single country, Zanzibar joining Tanganykia to form Tanzania https://en.wikipedia.org/wiki/Tanzania#Modern the short-lived union of Egypt & Syria in the United Arab Republic: https://en.wikipedia.org/wiki/United_Arab_Republic (There are probably more: this is just off the top of my head.)

The present US state of Texas was (at least in its own eyes) an independently sovereign country from 1836 until joining the US in 1846. Mexico never really recognized its independence and there was ongoing conflict, the US recognized it from 1837. It is worth noting that (at least in most tellings) the goal was always to join the US, but politics within the US prevented that from immediately happening.

A small region of California considered itself independent for a few weeks in 1846 (again, pre-statehood) though this does not seem to have been recognized by any other power.

Although those situations are effectively settled in history, one thing they demonstrate is that "independence" is to some extent subjective. There are disputes in the world today that, at least in some eyes, follow a similar pattern where a region claims to have broken away from country with the goal of joining another, often with the separation enabled by at least informal aid from the intended destination country.

A less disputed example could be the case of the German Democratic Republic (aka "East Germany") which chose to dissolve and join the Federal Republic of Germany (aka "West Germany") in 1990. Still, it is tempting to ask if the fact that reunification did not happen sooner, was because the GDR had not been fully sovereign and self-determinate - when it became practically so in 1989, reunification proceeded quickly.