I think one of the reason why there were few cats around is because they used to eat them. And once in a while the restaurant pet cat catches would grab an pet cat they may find and take them back again to the restaurant. I remember seeing cats in glass shows out the front of the restaurants. But somewhere between then and now they forbidden eating cats. So cats are now not on the menu and now there are cats everywhere. Most of them began 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 tummy worms would have been a problem. Fleas are not a really problem because they have got tile surfaces and real wood furniture.
Then your nine lives of the humble kitty who only wished to help mankind by eradicating rodents that carried disease took a serious switch for the worse during the dark ages. Where witch hunts and burning at the stake were typical. Somebody who didn't like pet cats somehow connected them to witches and they were burnt at the stake with there owners. That they made that connection I'll never know. It began with Pope Gregory IX in the 1232 who regarded the common house kitten as diabolical. Then to make things more serious in1484 along came up the greatest kitten killer ever, Pope Innocent VIII, who decreed something such as all cats came from hell and really should returned to the fires of hell by flame. Felines were mercilessly prosecuted and were burnt so they might return to the fires of hell. It is amazing any survived because if you were caught with a cat you were burnt collectively. I still go to cathedral and sometimes I just wonder why. And undoubtedly the Black Death was in the backdrop surviving and thriving because there were no pet cats to kill the rats that carried the fleas that caused the condition. Then along arrived the cat's savior Ruler Louis XIII of France, who in the 1630s repealed the law and cats once more started to live. But they were still hated and killed for many ages after that. I have no idea if the Dark Loss of life subsided but felines once again protected mankind from the diseases carried by rodents. Plus the famines brought on by mice plagues.