What is the significance of the dog in "There Will Come Soft Rains"?

The science fiction short story "There Will Come Soft Rains" by Ray Bradbury tells of a single house still standing in a decimated city after a horrifying atomic war. The house goes through its automated routines, making breakfast, washing dishes, cleaning the rooms, disposing of garbage, and urging children to go off to school and adults to go to work.

Outside, a charred wall tells the graphic story of what happened to the humans who lived there. The entire wall is burned except for silhouettes in white paint of a man mowing a lawn, a woman picking flowers, and two children playing with a ball. They must have been incinerated in an instant as a bomb struck the city.

The significance of the dog is that it is the last living inhabitant of the house. The house is very secure and protective, but it recognizes the dog's voice and lets it in. This indicates that the dog was the pet of the humans whose silhouettes remain on the outside wall. In the aftermath of the devastation, the dog has nothing to eat and is starving. Its death is symbolic of the cessation of the house's reason for existence. It was created to serve the humans and pets that lived in it, and now they are all dead.

Bradbury then personifies the house as he describes its death. A tree bough breaks a window, a fire starts, and the house burns down. In this tragic anti-war story, Bradbury contrasts the efficiency of the house, which should have made life pleasant and easy for its human and nonhuman inhabitants, with the terrible results of a destructive war.

What is the significance of the dog's condition in "There Will Come Soft Rains"?

The dog is dying because it is one of the last creatures left alive after surviving a nuclear blast.

The dog is in very bad shape.  The world has undergone a nuclear event of some sort, so that the inhabitants of the house were reduced to spots.

The five spots of paint—the man, the woman, the children, the ball—remained. The rest was a thin charcoaled layer.

That is all that remains of the family that used to live in the house.  The spots are where they were standing when the blast hit.  The dog survived though, but he is suffering the effects of nuclear exposure.  He is dying.  Sadly, he tries to get into his house and find his family, but he doesn’t realize they are dead.

The dog ran upstairs, hysterically yelping to each door, at last realizing, as the house realized, that only silence was here.

As the house makes pancakes for a family that no longer exists, the dog dies.  The house’s electronic mice come and clean it up.

This is significant because there are no human beings left, and there are now no living creatures left.  The robots have taken over.  They have no sympathy when the dog dies, sweeping it up like garbage even though it is a living creature.  It is remarkable that the dog survived so long, but it gets no credit for its achievement.  Its only reward is the sad realizable that it has outlived the family it loved, and is trapped in the automated emotionless world of the house.

Like many of Bradbury's stories, this one tells a cautionary tale of technology versus humans.  The most touching moment in this story, or perhaps the most jarring, is when the dog's body is removed by the robot mice who do not distinguish it from other garbage.  The contrast between the dog crying for his missing family and his realization that they are not coming back and the mice, who used to make the family's life easier, throwing him away, is a sharp one.  The very technology that makes human life easier can also destroy us.  It is what made the bomb that killed everyone but the robots, we assume.  

Why did the dog in "There Will Come Soft Rains" react in that particular way?

The date is August 4, 2026. The house is technologically advanced to the point that almost everything is automated. The house continues to function according to all of its programming even though the entire family has died. Given the evidence of their silhouettes outside the house and the "radioactive glow," there has been an atomic explosion. So, the family and everyone in the city has been killed. If this had been part of a larger bombing and/or atomic war, more people are probably gone as well. Somehow, the dog has survived the blast. 

The dog comes into the house looking for its human family and hears only silence. The dog might have suffered radiation poisoning from the nuclear blast and this could have lead to his death or at least contributed to the sores or even affected its appetite. But given the physical description and the fact that the dog was kept outside the kitchen door, it is more likely that starvation was the cause of death: 

The dog, once large and fleshy, but now gone to bone and covered with sores, moved in and through the house, tracking mud. 

It sniffed the air and scratched the kitchen door. Behind the door, the stove was making pancakes which filled the house with a rich odor and the scent of maple syrup. The dog frothed at the mouth, lying at the door, sniffing, its eyes turned to fire. It ran wildly in circles, biting at its tail, spun in a frenzy, and died. 

The once large dog is now skin and bones. Having been deprived of food for an inordinate amount of time, the dog is close to death. With its little remaining strength, the dog froths/salivates at the smell of food from the kitchen, desperately runs around out of frustration, and finally dies of malnutrition. 

Why does the dog react as it does in "There Will Come Soft Rains"?

In "There Will Come Soft Rains," the dog acts upon the conditioning that he has received. 

When the poor dog returns to the house, after having been subjected to radiation, he whines at the door which is made to respond to sound. Then, he searches the house for the occupants, but they are not in any of the rooms that they occupy. He, then, sniffs the air and smells the pancakes. so, he runs to the kitchen where the occupants usually convene to eat.

The dog frothed at the mouth, ...It ran in circles, biting at its tail, spun in a frenzy, and died.

The poor dog has suffered from radiation and its nervous system has been attacked; therefore, he acts with frenzied movements. Not unlike the animals on the nursery walls that glow, the poor dog is close to glowing, too, as he has been subjected to the nuclear explosion that has plastered the people against the wall in silhouette.