This documentary film (made by and for the National Film Board of Canada) is now impossible to find a copy of, impossible to pay to see via streaming services, etc.
https://www.nfb.ca/film/letters_from_karelia/
The topic here is taboo in the extreme, whereas "the opposite" story is commonly told: ethnic Finns and Karelians escaping from Communism in the Soviet Union / Russia (to live in Finland itself, or sometimes in the United States and Canada).
The reality is that people moved in both directions: there were Finnish and Karelian people voluntarily signing up to become a part of the utopian experiment. To what extent those people were honest with their children and grandchildren thereafter is an open question.
Keep in mind that even in Japan there were always a few Japanese and Ainu (in each generation) who would flee north over the Sakhalin Island border to sign up for Soviet citizenship, voluntarily.
My impression is that Finns still exoticize Karelians, regarding them as significantly different from the Finns of the west coast —not merely in their accent and religion but even in their physical appearance.
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The 2005 documentary Letters from Karelia (directed by Kelly Saxberg) chronicles the tragic "Karelia Fever" of the 1930s, when hundreds of idealistic Finnish Canadians emigrated to the Soviet Union seeking a socialist utopia. It centers on the personal story of Aate Pitkänen, an electrician who left Thunder Bay, Ontario, for Karelia in 1931.
While many migrants faced crushing hardships, typhoid outbreaks, and Stalin's Great Purge, Aate's ultimate fate remained a mystery after he was separated from his family and disappeared in 1941. Over sixty years later, his unmailed letters from a Finnish prisoner-of-war camp were discovered. These letters reveal his dramatic journey from a communist pioneer and USSR ski champion to a Soviet spy, ultimately uniting his sister, Taimi, with the son he never met.
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