"Death solves all problems," declared Joseph Stalin, adding with his customary brutality: "No man, no problem." Anyone found guilty of threatening the Soviet state by his deeds or even thoughts would be eliminated. During the Great Terror of 1937-8 close to two million Russian army chiefs, priests, professors and other "enemies of the people" were shot or sent to the Gulag. The executions were carried out by many willing henchmen but Stalin was the dominant will behind them. With cynical adroitness, he set families against families; the children of Gulag internees were shut up in reformatories and often not heard of again. Their blighted personal lives ill-conformed to the Stalinist ideal of a happy childhood.

For all his cruelty, Stalin was not delusional. He knew very well that "confessions" extorted from his so-called enemies were only rarely true. (One victim, Stalin liked to joke, had been persuaded under torture that he was the author of Eugene Onegin.) Unlike Hitler, Stalin did not see enemies everywhere: rather, he invented enemies because he needed them. Underlying his strategy of annihilation and persecution was the deeply rooted principle (inherited from Lenin) that enemies were more useful to Soviet power than friends. Stalin's power was in fact directly proportional to the extent of the perceived enemy threat, whether it was kulaki peasant proprietors, American spies or, later, Jewish doctors.

It was not difficult for Stalin to seek out his enemies. By the dawn of the 1950s some 10 million spies were operating in the Soviet Union. Information was gathered on so-called "wreckers" in every walk of life – name, address, profession – and set down with lapidary coldness in official communiqués. Fearing guilt by association, friends distanced themselves from each other. The Bolshevik virtue of tverdost – hardness – demanded an indifference to the trap door disappearance of those you loved.

In Just Send Me Word Orlando Figes tells the true story of two young Moscow scientists, Svetlana Ivanova and Lev Mishchenko, whose love for each other endured the Gulag and Stalin's attempts to "reforge" them into dutiful Soviet citizens. Neither Svetlana nor Lev was at heart anti-Soviet; they believed in the forward march of the "new Soviet man" through technology, and at first they revered Stalin as the great vozhd (leader) of the Russian people. Fiercely motivated and bright, Svetlana saw in Soviet communism an intellectual calling and hope for the future.

All that changed in June 1941 when Hitler invaded the Soviet Union. The carnage as German troops advanced across the Stalin line was appalling: roughly 27 million Soviet citizens were to perish in the conflict they called the great patriotic war. Lev hurried to sign up in defence of his country, and showed great courage as a Red Army officer in the forests near Smolensk. He was captured by German troops, however, and interned in Buchenwald, where the guards beat the prisoners with a bestial insouciance (using rubber truncheons that left no mark on the skin).

At the war's end, in spite of all he had suffered, Lev was interned in the Gulag as a suspect German spy. It made no difference to Stalin's interrogators that he was innocent. Convicted of "treason to the motherland", he was given 10 years in the corrective labour camp of Pechora in the far north of Russia. Other enemies were "purged" (a euphemism for judicial murder which the Soviet dictatorship has added to the language) or else sent to die in the frozen immensity of Siberia.

Against all the odds, Lev managed to smuggle letters out of the Gulag to Svetlana back in Moscow. He did not think of the possible repercussions for her in receiving correspondence from a convicted "enemy of the people": he lived for "Svet" and ignored all risks. As Lev persisted with his secret correspondence he began to receive post in return from Svetlana. The letters gave a slender meaning to his life and a sense of a connection to the world he had lost. He concealed them beneath floorboards in his barrack.

Fortunately, the correspondence is preserved in its entirety in a Moscow archive. Running to some 1,246 letters, it is the biggest known private collection relating to the Gulag. From it, Figes is able to build a picture of life in Pechora with its watch towers and isolation cells, where violence was the language understood by all.

Lev is initially shocked by the "criminality" shown by his fellow inmates. The prime stimulus in the camp was to find food; the food either had to be stolen or bought from the camp's gangster elite. Very few prisoners were able to remain faithful to the "decencies" they had left behind in the free world. "You really do become a savage and malicious animal," Lev wrote to Svetlana, adding that he would have been appalled by the thieving as a free man (in the Gulag, thieving was considered a matter of pride).

The guards were often drunk and violent, yet the violence was administered less out of hatred than out of routine, Lev suggests – the way a man might beat his dog. The arbitrariness and cruelty of tsarist authority had found its grotesque mirror image in the labour camp: day to day, prisoners had no idea what would happen to them. When Svetlana visits from Moscow one day, having made the 900-mile rail journey to Pechora without official permission, Lev can scarcely contain his excitement. "My Sveta, how wonderful it is that there is you… I see only you."

On his release in 1954, however, one year after Stalin's death, Lev appears to be disorientated and mildly depressed. After the nightmare intensity of the Gulag, everything seemed colourless, futile and false to him. "He felt none of the euphoria he might have expected," Figes comments. "In some ways he was sad to be leaving."

Lev had grown up dreadfully during his Gulag captivity. His innocence and much of his emotional life had been ripped out of him. Yet, in some awful way, the Gulag was his university and the place where he learned the ways of the world.

He was overjoyed to be reunited with Svetlana but, like all exiles, he felt that he had come back to a different world that had moved on without him. Everywhere he went in Moscow, employers were suspicious of his "criminal record". There was no glory in having been a Gulag internee; the shame was indelible.

But in 1956 his fortunes changed when Khrushchev denounced Stalin and his "cult of personality". The unmasking of Stalin as a dictator was a turning point for the 20th century; with it, the die was cast for Gorbachev's glasnost in the mid-1980s.

Having married Svetlana, Lev was finally able to return to his pre-war work at Moscow University's Institute of Nuclear Physics, where he stayed until retirement. When, in 2008, Figes visited Lev and Svetlana in Moscow, he found a contentedly married couple who had come through hard times together. Just Send Me Word, grimly absorbing, conveys the pity of the Stalinist Gulag with integrity and proper sympathy.

Ian Thomson's biography of Primo Levi is published by Vintage.