We don't have exact numbers as to how many Soviet POWs were taken by the Finnish forces in 1941-1944. The total number has been estimated as 67 000. There are some estimates that up to 5700 Red Army soldiers might have died/been killed before being registered as prisoners of war in the first place.
During the war, c. 19 100 registered Soviet POWs died in the Finnish POW camps. (This would then make the total mortality 28,5% of registered POWs, or, up to 35% of all captured Red Army soldiers in Finnish hands, accounting for the potentially not registered ones). 14 700, over 77% of all mortalities, happened in 1942.
There are many reasons for the massive death toll of 1942, and a lot of it can be explained by a combination of not being prepared for such large numbers of POWs and having a hostile, often racist attitude towards Russians due to history, propaganda and the feelings brought up by the losses of the Winter War.
The poor food situation of 1942 also contributed to the deaths - during a year when the civilian population faced near-famine conditions itself, the hated Bolshevik soldiers only got comparative scraps of food, including animal feed and substances that should not have been fed to even dogs. The result was starvation or near-starvation for thousands. The camps, due to the poor preparedness, had inadequate (and sometimes nearly non-existent) shelter and the winter was harsh. During the first year, camp hygiene was also bad and disease rampant. The POWs were also made to perfom hard physical work like logging, to keep the Finnish war economy going.
This combination, in 1942, led to mortality that rivalled Nazi POW camps, even if only a very small number of the Soviet POWs in the camps died due to violence. According to wartime statistics, for over half of the deceased, one or other disease was marked as the cause of death. We can say that there was no official policy or orders to kill as many prisoners - but neither was there actual will or effort, in the event, to stop the mass deaths in 1942.
The conditions and deaths in 1942 still led to various improvements in 1943-44, and even though in 1943-44 the Finnish camps still held c. 40 000 Soviet POWs, during these years only a bit over 1000 POWs died - meaning that post-1942, the conditions in the Finnish camps improved dramatically and remained reasonably good until the armistice.
Summa summarum - for a Soviet soldier getting caught from the summer of 1941 to October-November 1942, Finnish captivity would prove lethal in roughly one third of all cases. But be lucky enough to survive to November 1942 or so, or be caught by the Finns in 1943-44, and you'd have better chances of returning safely back to the Workers' State in late 1944 than in pretty much any other realistic role a Red Army soldier could have in those years. What would happen after it would be another question.
And then to the civilians in the occupied area. In 1939, the Karelian ASSR had 470 000 people. According to my sources, "the most inhabitants" in the area the Finns occupied in Eastern Karelia were evacuated at the start of the Continuation War. As a result, the area had 86 000 Soviet citizens when it was occupied - even also considering the effects of conscription, etc, that means a major evacuation effort. Due to the evacuations, the make-up of the remaining population skewed towards women, children and the elderly - getting out military-age men had been practically best achieved, it seems.
Of these 86 000, 36 000 were deemed Finnic - Karelians, Ingrians, Veps or Finns (or even smaller groups). The rest were mostly Russians. Of the non-Finnic population of 40 000, a major part was then placed in the so-called concentration/transfer camps for reasons of security (diminishing the chance for partisan activity, etc) and in expectation of eventual resettlement to "Russia proper". At worst, in March 1942, c. 24 000 people was moved to these camps. After that, the number fell - by early 1944, the camps held half of that number. During the entire occupation, nearly 4300 people died in the camps, due to various reasons, which corresponds to roughly 18% of the highest number.
Now, the mortality in the camps is said to be circa five times that than in among the rest of the population in the occupied area, and ten times that than in Finland itself. This means that while the conditions in the camps were horrid, especially during 1942, the time of the biggest mortality, mostly due to a combination of poor nutrition, disease, inadequate shelter and hard work, in the other parts of the occupied area, the wartime mortality was only twice of that within the 1940 borders of Finland.
The Finnish policies towards the occupied areas were a far cry from what the Nazis did - all through the occupation period, the Finnish actually authorities tried to improve the conditions in Eastern Karelia. That was due to the fact that a great number of the people here were "kin" to the Finns, and that Finland aimed to eventually join the area to itself as ordinary provinces according to the prewar model. Even in the camps the conditions improved after 1942 so much that by mid-1944 their mortality was not significantly above the general numbers of the occupied area. There was a great effort to fight against infectious diseases, for example, especially typhus, in Eastern Karelia. The effort, we can argue, left the occupied area better off in terms of disease prevalence in the fall of 1944 than it had been in early 1941. The Finns used Zyklon B, too - but only to kill actual lice, quite successfully. In the last parts of the war, especially 1944, we can also say that treating the Russians in the occupied area increasingly better was also due to cynical expectation that if the USSR wins the war, doing this would avoid some of the measures of retribution by the Soviets towards Finland.
In the light of these numbers, I'd say that in order to survive the occupation of different parts of the USSR during WWII, one probably had the best chance if one lived in the Karelo-Finnish SSR in 1941 and managed not to be sent to the camps the Finns set up for the non-Finnic civilian population. And even in the camps, terrible and arguably criminal as they were, one would have had an over 80% chance of survival.
(The numbers above are mostly from Sotavankien ja siviili-internoitujen sodanaikainen kuolleisuus Suomessa ["The Wartime Mortality of Prisoners of War and Civilian Internees in Finland"], a study by Doctor Lars Westerlund, a docent of justice and administration history at the Åbo Akademi, published by the Finnish Historical Society in 2009.)