My daughter and her husband have three cats. Two adopted rescues and one they rescued themselves. That is a story in itself. He showed up at their house and wouldn't leave. They never let him in, but he hung around was very sweet and loving to everyone who was out in the yard. Eventually because Winter was coming, they got him checked out by a Vet and adopted him.
Fast forward to my babysitting. The Dude, mentioned above, has always been sweet and very friendly. Nermal, the female, is friendly after a while. But Lemmy is very shy. He hides when anyone comes in the door, and doesn't come out until they are gone.
Recently, I was astonished to find Nermal interested in my knitting. I was sitting on the couch, and she came over and laid down with her front paws on my left leg. She played with the yarn while I knit. Nermal has been on me before, usually she uses me as a bridge to get from one place to another. But later that day, she actually came up and laid down on my lap! I was so excited, I took a photo with my phone and sent it to Sara. I was really thrilled.
But there was more to come! She got up, and turned to face me. She put her front paws on my chest, and I petted her with both hands, from the head down. Then she leaned forward, close to me, and licked my nose! Apparently that's what she does. Sara warned me that she might give me a little love bite, but she didn't that time.
Lemmy finally felt comfortable enough with me in the house to make an appearance after the second week. He had been hanging out on the basement steps. I would open the door and talk to him, just to get him used to me. When he finally came out, I would just pet him once as I walked by, not pushing my luck. Now he will come into the living room and sleep on the recliner with The Dude. I get to pet him a little and he doesn't run away.
I feel that I have been accepted into the family clowder. I had to look that word up. It's what a group of cats are called.