Naum Faiman was born in 1913 near Odessa, Ukraine, in a Jewish family. He was one of four siblings, and his parents worked in agriculture. The family initially owned a small plot of land. Later, they partnered with several other families to cultivate a larger plot. During the Soviet period, this partnership became the basis for a Jewish kolkhoz (collective farm). Its existence was made possible through the financial, organizational, and agronomical support of the American Jewish Joint Distribution Committee, which had begun to sponsor Jewish agricultural projects in the USSR in the mid-1920s.
When Naum was fifteen, his father Abraham was killed. The widow, Frida, now had to raise all four children on her own. Naum finished five grades of Yiddish school in his hometown, and was then apprenticed to a hatmaker. In 1935, he was drafted into the Red Army, and served for three years as a machine gunner in the Soviet Far East. By the end of the 1930s, many Jewish kolkhozes had become "internationalized" (i.e., merged with Ukrainian ones), and Naum decided to move to Odessa, where he began to work at a hat factory.
In November 1941, some five months after the German invasion of the USSR, Naum was sent to the front lines near Moscow and assigned to a sapper brigade, where he had to lay and clear mines. In this capacity, he saw action in the North Caucasus and Ukraine; on the Baltic and Leningrad Fronts; in Malaya Zemlya, and in East Prussia. In 1943, he was promoted to starshina (sergeant major). Once, when his soldiers were encircled, he managed to break through and save them all. For his service, he was awarded the Order of the Red Star.
When the war was over, Naum returned to Odessa. His two brothers had been killed in action, while his mother, along with other relatives of his, perished in the ghetto. He resumed working at the hat factory that had employed him before the war. Shortly thereafter, he married.
In 1990, Naum Faiman and his wife moved from the USSR to Israel.