Since the entire book takes place in the prison camp, we only hear about Shukhov's wife second-hand, from Shukhov himself. Unlike a lot of people's families, Shukhov's has not abandoned him. But they don't send Shukhov aid packages either, at his own request.
It had been easier for Shukhov to feed his whole family as a free man than it was to feed just himself in the camps, but he knew what those parcels cost, and you couldn't go on milking your family for ten years on end. Better to do without. (925)
Shukhov's relationship with his family reveals a lot about his character. It shows that he's an honorable, decent, and un-selfish person.
But Shukhov's wife isn't just a means for demonstrating how cool Shukhov is. She's a character in her own right, even if we hear fairly little about her. The fact that she writes to Shukhov dutifully, twice a year, and has hopes and plans for when he returns home tells us a lot about her. In a lot of ways, she is like Penelope, Odysseus's wife in the Odyssey who waited twenty years for him to return home, remaining faithful the whole time.
Shukhov's wife struggles daily with poverty and can scarcely understand her husband's life, just as he can scarcely understand hers. It's like a huge chasm or an ocean exists between them; and it's no mistake that Shukhov uses a water metaphor to describe his letters home as stones sinking in bottomless pool (224). But even though she can't grasp what he is doing now, she still considers Shukhov a part of her life and still makes plans, however futile, for when he finally makes it home.