Can stray cats smell or sense when your pet has started the dying process?

I’ve heard cats in nursing homes will sit outside a door or lay next to a terminally ill patient only for the person to pass soon after. Do they do this with pets too?

I’m only wondering because a few days prior to my dogs tumor ulcerating and then him declining rapidly the next week until I helped him pass at the vet, a stray cat showed up on my patio one night trying to get in. I have never seen a stray cat at my complex, and I haven’t heard from it or seen it since that night. I ended up calling the cops on a cat because it sounded like someone was trying to break in. Of course it didn’t start meowing or howling until after the cops confirmed it was a cat. lol But it was trying all night to get in getting more aggressive about it throughout the night to the point it sounded like it was throwing itself at my sliding glass door. I would’ve let it in but I didn’t want to stress my dog out or have it bring in some infection or something to him since he was old and had cancer.

At that point I thought my dog was fine for the moment, even though I knew his time was coming. He was sleeping a little more than usual but it wasn’t concerning. Just figured little elderly man sleeping. He was still acting like himself and eating and drinking like normal. I didn’t think anything of it at the time other than maybe the cat used to live here previously and just now decided to wander back? And then the day before I had to put my dog down it kinda clicked in my head well maybe it was doing what cats do in nursing homes…?

Did the cat smell something in his urine or poop outside that signaled death? Or does the body start releasing or producing more of certain hormones or chemicals in the body to signal the start of the dying process?