The cat in the Gordimer story represents both a representation of domestic bliss, but also the imprisonment that is experienced when fear controls every aspect of being in the world.
When Gordimer initially sits down to write her fairy tale, she opens it with a blissful representation of domestic life. The family is very happy and the cat is a significant part of it:
In a house, in a suburb, in a city, there were a man and his wife who loved each other very much and were living happily ever after. They had a little boy, and they loved him very much. They had a cat and a dog that the little boy loved very much.
In this construction, the cat represents happiness and a sense of contentment. The world of the family includes children and pets, of which the cat is a part.
However, as the fear of crime begins to loom over the family, there is a greater desire to insulate themselves. They wish to cut themselves off from a world that they fear. Their anxiety dominates all of their decisions. This culminates in the building of the wall with "razor bladed coils" so that it could not be scaled. The husband and wife discuss how the cat is going to react to this change:
And she waited until the little boy had run off to play before she said, I hope the cat will take heed ... The husband said, Don't worry, my dear, cats always look before they leap. And it was true that from that day on the cat slept in the little boy's bed and kept to the garden, never risking a try at breaching security.
The cat represents the curtailed condition of freedom enveloping the family. Just as the husband and wife grow increasingly skeptical of the world around them, the cat is forced to adopt the same mentality. The cat can no longer freely climb and roam where it wishes to. Instead, it must retreat to sleeping on the boy's bed because the world outside- one that was built by the husband and wife out of fear- is filled with dangerous elements. The cat's perception represents the fear of "the other" that is a critical aspect of the parents' understanding of the world and their place in it.
Finally, the ending of the story shows the cat supporting the theme of fear of "the other" in how it trips the alarm. The cat is the one who sets off the alarm. It is a wailing sound that mirrors how the husband and wife see the "bleeding mass" that is their son. The cat activates the alarm and with it, displays how the family's desire to protect themselves have actually done harm to one of their own.