Hey there, /u/Vladith. In short, most of them left.

In long, most of them weren't settlers as you think of them. Russian America, because it was operated by the Russian-America Company on a for-profit basis, needs to be compared to northern Canada and other territories operated by the Hudson's Bay Company — not the British colonies that became the United States.

The purpose of Russian America was to make money for the RAC's shareholders, not to provide settlement space for Russia. Imperial Russia, stretching from Poland to Canada, had more than enough space already.

Because of this profit-minded approach, there were never that many Russians in Alaska. More Russians would have meant more expenses for the company. Instead, the company relied primarily on a network of creole Natives — half-white, half-Alaska Native. There were few — likely 1,000 or fewer — white Russians in Alaska at the time of the Alaska Purchase.

Many of them left Alaska when the purchase took place. This took place despite Article III of the purchase treaty, which states:

"The inhabitants of the ceded territory, according to their choice, reserving their natural allegiance, may return to Russia within three years; but if they should prefer to remain in the ceded territory, they, with the exception of uncivilized native tribes, shall be admitted to the enjoyment of all the rights, advantages, and immunities of citizens of the United States, and shall be maintained and protected in the free enjoyment of their liberty, property, and religion."

Universal citizenship for Alaska Natives didn't occur the Indian Citizenship Act of 1924.

By the 1880 U.S. census, the first in Alaska, there were only 430 "white" individuals. Note that this does include a small Russian farming community at Ninilchik on the Kenai Peninsula. Ninilchik was a big exception, as Russian America derived most of its food from California and Oregon as far back as the start of the 19th century. The Russians were abysmal failures at turning Alaska into a self-sustaining operation.

Where did the Russians go? Many of them went to the Amur River basin, which had just been taken over by the Russians in a series of treaties with China. That area had much of the promise of Alaska, but it was on the same side of the Pacific as Moscow and thus seemed to offer as many advantages with fewer disadvantages.