Atul Gwande's book that turned me onto this one - he described it as required reading as a med student, and a powerful description of a person going through the dying process (mentally, not physically). It makes sense that there would be little good literature on the experience of dying, since those going through it are generally not in a condition to write about it, nor do they make it out the other side in order to describe it. (One recent counter example that comes to mind being Oliver Sack's essays as his condition worsened over time). Tolstoy's work is fiction, but well executed. He focuses on death, not as an abstract occurrence that happens to everyone, but as an intimate and personal affair that is experienced only (and by definition) by the individual. As they say - we all die alone. Tolstoy really digs into that loneliness. In a sense, people who are irrevocably dying share nothing in common with anyone living, even their most loved ones. No one truly empathizes with the damned. They have no future, and in so doing lose their humanity.
Some quotes:
Besides considerations as to the possible transfers and promotions likely to result from Ivan Ilych's death, the mere fact of the death of a near acquaintance aroused, as usual, in all who heard o it the complacent feeling that, "it is he who is dead and not I."
The syllogism he had learnt from Kiesewetter's Logic: "Caius is a man, men are mortal, therefore Caius is mortal," had always seemed to him correct as applied to Caius, but certainly not as applied to himself. That Caius - man in the abstract - was mortal, was perfectly correct, but he was not Caius, not an abstract man, but a creature quite, quite separate from all others. [...] Caius really was mortal, and it was right for him to die; but for me, little Vanya, Ivan Ilych, with all my thoughts and emotions, it's altogether a different matter. It cannot be that I ought to die.
The book is profoundly sad - in a very obvious "meta" sort of way. Because even as I read it, and I feel sad for Ivan, and I try to intellectualize the lesson and reflect on his death, and on death in general, in the back of my head there is very much a feeling of "it is he who is dead and not I." Ivan Ilych was mortal, and it was right for him to die; but for me, with all my thoughts and emotions.......