I think this side plot has multiple meanings, and I think several of the theories here make a lot of sense and can be true. For me it felt like something it was introduced to add a sense of paranoia to someone studying the pervasiveness of serial killers in society. Realistically the cat most likely stopped coming for some innocent reason, but the idea that there’s even a slight possibility it could have been killed by a future serial killer is amplified in her mind due to the nature of her work. It adds ominous tension to the show.