I believe one of the reason why there were not many cats around is because they used to eat them. And once in a while the restaurant kitten catches would grab an cat they could find and take them back to the restaurant. I recall seeing felines in glass displays out the front of the restaurants. But somewhere within then and today they suspended eating pet cats. So cats are actually not on the menu and today there are felines everywhere. Many of them started off in someone's house and got thrown away, because so many are incredibly friendly. Also they have this thing about abdominal worms. And in those days China was not as modern as now so stomach worms would have been a problem. Fleas aren't really a problem because they have tile flooring surfaces and wooden furniture.
Then your nine lives of the humble pet cat who only wished to help mankind by eliminating rodents that carried disease took a significant change for the worse during the dark ages. Where witch hunts and getting rid of at the stake were the norm. A person who didn't like felines somehow connected these to witches and they were burnt at the stake with there owners. How they made that interconnection I'll never know. It began with Pope Gregory IX in the 1232 who considered the common house cat as diabolical. Then to make matters more serious in1484 along emerged the greatest cat killer of all time, Pope Innocent VIII, who decreed something such as all cats came from hell and really should delivered to the fires of hell by fireplace. Pet cats were mercilessly prosecuted and were burnt so they would go back to the fires of hell. It really is amazing any survived because if you were trapped with a cat you were burnt mutually. I still go to church and sometimes I simply wonder why. And of course the Black Death was in the background surviving and growing because there were no cats to get rid of the rats that carried the fleas that brought on the disease. Then along came up the cat's savior King Louis XIII of France, who in the 1630s repealed the law and cats once more started to live. However they were still hated and wiped out for many decades after that. I don't know if the Dark colored Loss of life subsided but felines once again shielded mankind up against the diseases taken by rodents. Along with the famines brought on by mice plagues.