The butcher was alone in his shop when she came in and was annoyed by the thought of such a sick-looking old woman out on such a day (2.13)
Although the butcher is actually nice to Mrs. Grimes, the fact that he's "annoyed" is telling. It's almost as if he knows that she's dying but doesn't want to deal with it. A pretty depressing thought.
The running of the dogs may have been a kind of death ceremony. It may have been that the primitive instinct of the wolf [...] made them somehow afraid (3.13)
The dogs are closer to the natural world, which makes them closer to the reality of death. They don't fear it, like we do—they know that it's just one step in the circle of life.
The dogs were waiting for me to die as they had waited for the old woman that night [...], but when it happened to me I [...] had no intention whatever of dying (3.16)
This raises an interesting question—does Mrs. Grimes want to die? Is she so beaten down by life, so tired of her abuse, and so hopeless about the future that she's ready to give up?
The old woman died softly and quietly. When she was dead and when one of the Grimes dogs had come to her and had found her dead all the dogs stopped running (3.16)
Mrs. Grimes isn't necessarily afraid of death. In fact, the first stages of the process seem a lot like going to sleep. Maybe that Shakespeare guy knew what he was talking about after all.
Well, she was dead now. She had fed the Grimes dogs when she was alive, what about now? (3.18)
This quote has a double-meaning. On one hand, it's referring to the literal dogs that are running around Mrs. Grimes' body. But don't forget, if anyone has earned the title of "dogs" in this story, it's Jake and his son.
When she was found, a day or two later, the dress had been torn from her body clear to the hips, but the dogs had not touched her body. (4.3)
Mrs. Grimes is left naked and exposed after her death. She has literally given all that she has for the sake of others, and now she's left with nothing but her own self.
Her body was frozen stiff when it was found, and the shoulders were so narrow and the body so slight that in death it looked like the body of some charming young girl (4.3)
Remember: the narrator has already told us that Mrs. Grimes is only around forty, though she looks way older. After her death, the stress that caused that premature aging simply evaporates.
As a matter of fact, the hunter had not looked closely at the body. He had been frightened. She might have been murdered and some one might spring out from behind a tree and murder him. (4.9)
What a tough guy. Although the townsfolk act super manly, they're just as shaken up as the narrator and his brother—two children. But death has a way of making children out of all of us.
Her daughter had died in childhood and with her one son she had no articulate relations. On the night when she died she was hurrying homeward, bearing on her body food for animal life. (5.14)
This is the long and short of it. She fed men and livestock during her life; she fed the natural world with her death. This emphasizes the fact that death is an integral part of the life cycle.