What is the “reproach to the living” on Ivan’s face mentioned by the narrarator at the beginning of the story?
Ivan's reproach to the living is seen in his facial expressions that reflect his disapproval of the lifestyles of his family and friends. As his death comes closer, he becomes angry at his family for their superficiality and shallowness. Their lives actually mirror Ivan's own life, but it takes him a while to realize this. With hatred in his eyes, he tells his wife to leave him alone and let him die in peace. Ivan is disgusted by the importance they place on material things, even though he's partially responsible for their attitudes. In trying to find answers to the questions that plague him regarding how he lived his own life, Ivan realizes that perhaps he "had not spent his life as he should have done". In the end, Ivan's anger and hatred for his family changes to compassion and love when he finally sees "the light". He tries to ask for their forgiveness, and it's only then that Ivan is able to let go of his life and family.
As he approaches his own death, Ivan Ilych becomes aware of the fakeness of people around him, and of his own life as well. Though he has lived according to propriety, he realizes his existence has been a shallow one devoted to the pursuit of social status, while he has harbored a selfish indifference to the needs of others. He remembers his failure to sympathize with his wife's discomfort when she was pregnant as he rails against the seeming callousness of those around him (they go to the opera!) as he lies dying. He sees also the irony that he sustained the injury which is killing him while decorating his new house, symbol of his life's vain striving for wealth and position.
This is the 'reproach' - that in death Ivan knows the truth of his and his peers' futile lives, while they will continue to deny its application to themselves until it is too late.