Some years ago, when I was still living with my mom in a small town, we found a stray cat (how we found this cat is another story, but probably also nice to tell) and adopted it. We named him Cicero.
Cicero never got along very well with other male cats in our area; they were usually fighting or at least eyeing each other suspiciously when they met on the road. Especially the oldest male cat around whose name was "Mistake" was an arch nemesis for Cicero and vice versa.
Mistake was really old. His owners living a few houses away stopped caring about him and our neighbors sort of adopted him. He got slower and weaker every day and after a tumor had to be surgically removed, he mostly stayed indoors with his adopters. Sometimes he would sit on their doormat as a vantage point, occasionally being petted by passers-by.
One day our neighbors told us that Mistake had been becoming weaker and weaker and that they preferred to keep him indoors, otherwise something might happen to him (being run over by a car or something). The vet had told them that metastases had been found in Mistake's body and that it doesn't really make sense to operate on him again, since he was so old anyway. Mistake's days on Earth's surface were numbered.
Another day, when me and my family were coming home from shopping or something, Mistake was perching again on the doormat. Cicero had been welcoming us at the parking lot and walking us home. When Cicero spotted Mistake and vice versa, Cicero suddenly came to a halt. Mistake was startled, he thought that Cicero was up to a brawl again. Cicero slowly moved towards Mistake. Mistake was gripped by fear, got up and thought about running away.
But Cicero continued approaching. When he finally reached Mistake, he surprisingly rubbed his face on Mistake's. He did that two or three times. Mistake was paralyzed and didn't move. After that, Cicero came back to us and we continued walking home.
We were all moved by that. It showed us that cats can be compassionate, and that they can feel when somebody is ill. Wow... I love cats!