I have owned lots of cats in my life and yes if left to breed they can lead to this kind of squalor. It requires work to keep their litter area clean, their bedding area clean, and usually they will bed where they want to. You have to train them not to claw stuff, they go outside and get dirty from rolling around and bring the dirt back in. They are wonderful pets just like a dog but if you made no effort to keep a dog clean or housebreak it and then never clean up after it and let it breed constantly, it would be a bigger mess then these cats made. You can't get more pets then you can take care of. It will get out of hand. I still say this woman got overwhelmed and just let them go. It looks like she fed them cause there is food all over the place. The litter pan looks bad but it has been scooped out or it would have been full to the top with waste. I saw one like that once. The poor cat was crapping on top of crap. But if you figure 2 female cats have a litter each of say 5 kittens. Thats 12 cats. They can have 2 litters a year. If half of those are females, thats 7 females or 14 females in one year, thats just females. I haven't even counted the males. Then those 14 females will breed at 9 monthes each having around 5 kittens. So you see how she could have that many cats in just a few years.
I still think that there is something wrong with the woman. Cats may be immensely appealing, but no one in their full senses lets their numbers and one’s living conditions get out of control.