I have had cats all my life. Where we live now (on Okinawa) we have had between 12 or as many as 35 cats at once (we rescue). Many were not actually our pets, but stayed when they found they could get healthy food and occasional meds when needed. I've posted about some of them on A2K before, so some of you may be familiar with a few of our cats that became true pets.
We are down to about 15 cats now, and some of them are aged. We just lost our beloved Nemo to old age and organ failure (20 years old).
But I digress...
None of our cats ever brought down anything larger than a mouse, occasional rat, or a too-friendly and extremely stupid bird of small size. The cats we care for are well-kept, well-fed, and healthy. Even the strays that wander into our yard, abandoned by their departing American "owners", to find food and shelter, are rather tame. I think they feel no need to kill creatures they cannot eat, other than to express (affection? gratitude?) their feelings toward me and my wife. To date, they have killed nothing larger than a rat. Even that is seldom.
Cats chase small animals because they are bored or hungry. Owners who feed cats well and care for them (play with them, cuddle them, etc.) don't normally have large "gifts" left for them all the time.
But -- squirrels are no easy pushovers. They have sharp teeth, strong jaws, and are strong enough to grip and rip into even smooth bark. When a cat and a squirrel tangle, the cat stands a good chance of getting bitten, clawed, ripped, almost savaged. It isn't like catching a mouse, it's a life-death struggle. Squirrels do not give up easily.
So after dancing with a squirrel, the cat usually goes home wounded but "victorious". What happens over the next few days depends on how good the owner's vet is at stopping the infection, blood loss, maybe damaged organs,etc. Vet bills can add up.
Sometimes the vet says "Well, your cat tangled badly with a squirrel..." and the owner often blames the squirrel for attacking his/her cat...! So the owner takes action via poison, or calls a pest control agency, or complains to the city office.
It's possible too that the squirrels realize the new population of cats is a potential threat too their young, and have moved away to safer and "wilder" locations.
I suggest you call your local town or city office Animal Control section, and just ask if there has been a program launched to decrease or eliminate the squirrel population. Also, as mentioned earlier, poison may have been laid out for rats, etc., or other "pests" that may have a bearing on the squirrel population, and the squirrels just got in the way.
If you have seen that an apparently uninjured cat has killed a squirrel, it may have been a squirrel that was weakened or dying from some other cause (poison, etc.).