Q:

Who does the cat represent in Animal Farm?

It's well known that various characters represent real Soviet figures. Who does the cat, who is fond of shirking physical work but enjoys reaping the rewards, represent? Does the cat even have any significance in the novel?

A:

Yes. In the words of Jesse McDevitt-Irwin:

suggests that she could represent the educated of Russia, more specifically, the educated who did not believe that communism was the correct path. She also skips out on work, which could mean the educated because they did not do physical nature. One more clue is the nature of a cat on a farm: the cat performs a service (rodent control) and receives benefits (milk, shelter). This further implies that the cat was privileged under the Czars, which further implies the wealthy, educated class.

A:

The cat does have significance, but it's hard to say who exactly she represents.
She skulks around and doesn't do any work, votes for both sides, and makes people satisfied enough that she never actually has to do anything.

the behaviour of
  the cat was somewhat peculiar. It was soon noticed that when there was work
  to be done the cat could never be found. She would vanish for hours on end,
  and then reappear at meal-times, or in the evening after work was over, as
  though nothing had happened. But she always made such excellent excuses,
  and purred so affectionately, that it was impossible not to believe in her good
  intentions.

It seems like she represents the unhelpful people of society, the thieves and criminals and people who profit over other people's work.
There's someone of that kind in every society, who has no interest in the politics and leaves in the end. This cat represents all of those people.

everyone,
  indeed, except the cat, who had suddenly disappeared just before Napoleon
  ordered the animals to assemble.

A:

As acknowledged above, the cat probably represents opportunistic, underground criminals who persisted after the revolution. Her attempts to lure the wild birds by offers of camaraderie are simply a modified form of her (presumed) exploitation of weaker beasts pre-Animalism. Bribery was said to be ubiquitous in Soviet Russia and the cat managing to charm the authorities could well be a reflection of this. Her impunity also captures the confused relationship Marxism-Leninism had with crime; despite the totalitarian policing, criminality that wasn’t directed against the state was ideologically couched as a hangover of capitalism and to be regarded as a mental disorder. This is possibly why the other animals are so forgiving of the way she shirks work.
The fact that she is explicitly feminine and depicted as seductive may also be an allusion to prostitution specifically. Supposedly, prostitution surged after implementation of the New Economic Policy and initial attempts by police to crack down on the practice were foiled by the lack of recourse to any penal code; again, the failure of the pigs to do anything more than question the cat captures this ineffectuality.
Her non-appearance later in the novel could correspond with the clearer codification of a penal code in the Soviet Union and the attendent punishment of law-breakers, although personally I think she just carried on with her ways and since ultimately there wasn’t any more to say about underground crime under Stalin than in any other territory, Orwell didn’t elaborate on the allegory. 

