You never "own" a cat. The cat chooses to live with you.
Years ago, I had a cat named Murphy. I also had a cat named Yaz (there's stupid story behind that name). Then, I took in my brother's cat, Marilyn. So, there were three cats in a one bedroom apartment. I would let them out when I left for work & call them in for dinner.
One day, Murphy didn't show up for dinner. She didn't show up the next day either (yes, Murphy was female - there's a stupid story behind that name too). A few days later, I saw Murphy in the alley behind the apartment building. She came over, let me pet her, but wouldn't come back to the apartment. Later, I saw her in the window of the apartment across from mine. I figured out that she had decided that my apartment was too small for 3 cats and moved in with someone else.
When I moved out, I dropped off her papers with guy who lived there. He said she had just followed him into the apartment one day and decided to stay.
I hope she lived happily ever after.