The machines continued along their functions each day as progrmmed by the humans who were now deceased due to a nuclear explosion. Because humans are basically going to invent and create labor-saving devices in order to pursue leisure activities, these machines kill us in more than one way.
The labor-saving devices require that we have to do something physical in order to exercise enough to save our hearts and bodies from obesity, and the machines that move us around and manufacture our goods are polluters. So, the pollution from emissions causes climate change killing us in a completely new way, through starvation and famine and crop failure. The threat of nuclear war still hangs over us today just as it did in the 1950s.
At the time that Ray Bradbury was writing, nuclear war or the threat of nuclear war was eminent. There were drills and commercials on television with a catchy jingle, "Duck and cover" in order to avoid being incinerated by the first nuclear blast. But, just how many days did you have to stay under-ground in order to avoid radiation poisoning? No one knew for sure. Could anyone survive a nuclear war? I think Bradbury attempts to answer this question in his short story.
So, our playful family in "There Will Come Soft Rains" is destroyed leaving only shadows on their once beautiful home as a reminder that they actually existed. Their dog roams lonely and ill coming back to the place where he will be fed and watered by machines that are performing their function regardless of the need. Finally, the house is consumed by fire, a fitting end for the story.
If you think about it, the fire is the only warm thing about the story...it leaves you feeling somewhat cold. And perhaps that is Bradbury's intent. His writing seems calculated and mechanized in this story. He seems distant and detached as he describes in detail the mechanization that has overtaken these people's home life. And, we can only assume that this is normal for this society.