This reminds me of one of the stories in Ray Bradbury's The Martian Chronicles: "There Will Come Soft Rains". This is the most haunting of the stories in that book, in my opinion.

At the outskirts of city recently destroyed by nuclear war, there is a house. On the side of the house are the flash-burned figures of a family, mere shadows imprinted on a wall after the ravages of nuclear apocalypse. Inside the house, however, all of the little electronic devices that worked within it are whirring away, attempting to keep it running. Quickly, their systems break down. Reading it in seventh grade, this story changed my life. I had never read anything so beautiful in its simplicity of language and creative plot. This story made me want to write.

Although The Martian Chronicles do not even pretend to be scientifically accurate, I think that "There Will Come Soft Rains" offers some vital insight into the question above. Read it. I mean it, read it now.