Man's best friend plays a huge role in Disgrace, particularly after David moves to the country. On a surface level, they become characters in the novel. Some of the dogs that Lucy cares for in her kennel, like Katy the bulldog, have names and recognizable personalities. When you think about a little more carefully, though, it becomes apparent that they're not there as just your average canines; rather, Coetzee deliberately repeats the image of dogs as a way to emphasize the novel's interests in social status and personal disgrace.
On a broad scale, Coetzee employs dogs as a way to represent the statuses that various people hold in society. Lucy, for example, once says, "I don't want to come back in another existence as a dog or a pig and have to live as dogs or pigs live under us" (8.71). Sure, we all love dogs, but they live life lower on the totem pole than we do. Think of how dogs are used to characterize Petrus, as well; when we meet him, he introduces himself to David as the "dog-man" (7.55). At this point, he occupies the role of assistant to Lucy. As he ascends the social ladder, however, this changes. At his party, he jokes that he is "not any more the dog-man" (15.69). In one respect this is a tasteless joke about how all of Lucy's dogs were murdered – after all, he can't be the dog-man if there are no dogs to care for. At the same time, though, we can see this statement as an assertion of Petrus's growing social status: he's no longer on level with the dogs.
The opposite seems to happen to David. Though dogs are used to characterize his status, they more often reflect his personal, internal trials and tribulations. As things get worse for him and he dives deeper and deeper into shame and disgrace, his character becomes more closely aligned with that of a dog. When he talks to Lucy about his own humiliation at the University following his affair with Melanie, he compares himself to a dog that is beaten for following its sexual instincts (11.20-22). In a more concrete way, as David's personal situation worsens, he spends more and more time in the animal clinic helping to put dogs to sleep. On one hand, this act represents letting dogs out of their misery and suffering, but on the other hand, it's a truly pathetic way for them to go. Perhaps it's even more pathetic that David involves himself in the task.
As the novel winds down, the connection between dogs and people experiencing disgrace is made more explicit. Consider the following exchange between Lucy and David as they discuss the humiliation of how things have turned out:
"Perhaps that is what I must learn to accept. To start at ground level. With nothing. Not with nothing but. With nothing. No cards, no weapons, no property, no rights, no dignity."
"Like a dog."
"Yes, like a dog." (22.112-114)
To be a dog in this world is to be a base, low, helpless creature without rights or pride. Not long after this exchange, David becomes attached to one particular dog at the clinic that suffers from a crippled leg. Even though he sees disgrace in dying, he also sees extreme shamefulness in the way the dog is forced to live. The novel ends with David putting the dog out of his misery by giving it up to Bev for lethal injection. When he does so, we get the idea that he's in some way trying to save the dog from a life that is more disgraceful than death. We can't help but think that he does so in part to symbolically relieve his own sense of disgrace. The persistent presence of dogs in Disgrace pushes us to consider the shame and disgrace that humans go through, even though it plays out through the lives of animals.