Certainly they do. Cats don’t like change and they’re probably more aware of changes in their environment than we are. Cats have been known to detect medical issues in people like some dogs can, and this is probably due to a chemical or other change in that person. Cats don’t usually like change. They’re suspicious when the furniture is moved around, a Christmas tree is brought in, or there’s something new in the room. And they notice when someone or another animal is missing.
Ever try to move a cat? Even our evacuation experience during the fire of 2017 here in 
Ventura County was difficult for our cats. One of them even suffered afterward from what the veterinarian said was PTSD.
What about when someone or another animal moves out or dies? Does this affect a cat? Certainly it does. While the reaction is subtle in some cats, others will seriously mourn—they’ll stop eating, become more clingy, or they’ll withdraw from their human and their normal activities. Here’s a site with ideas for how to recognize when your cat is mourning and how to help him. https://www.hillspet.com/cat-care/behavior-appearance/do-cats-grieve
My mother had a neighbor cat visiting her and Smokey (her part ragdoll cat) for years. The tag on his collar said his name was Gibbs. Smokey didn’t seem to like Gibbs very much. He cowered when Gibbs was around, but he would wait at the sliding door for him to arrive each morning and he’d watch him with interest. There was a relationship there, even though we didn’t understand it. We became most aware of it when Gibbs stopped showing up. Either he moved with his family or something else happened to him, but one day he didn’t show up and we never saw him again.
Yes, that affected Smokey—something was different
and he knew it he and acted out some. It was subtle and it didn’t last for very long, but it was obvious that Smokey experienced something emotionally when Gibbs stopped his daily visiting routine.
That’s why we were concerned for Smokey when my mother died. While Smokey didn’t show much emotion outwardly or change in behavior, everything had changed for him. He was suddenly alone in the house with only visitors coming in to check on him and take care of things around the house.
One of Mama’s granddaughters came and stayed with Smokey for several days. Her plan was to bond with him—to help him bond with her while in familiar surroundings before she took him to her home to live with her family. Smokey had a lot of changes to deal with, but he adjusted, and he’s doing wonderfully. Some cats have a more difficult time, but there is help out there for the grieving cat.
