They always came back to you. I had many pets that died. And I am telling sincere with the hand on my heart: they came back to me, in form of another pet. I felt that, not just once but 3 times. Especially cats. That gives you more comfort and peace.
Honestly Darth this scares me, since I've experienced the exact same thing. We have a dog that my wife has observed, in passing, acts like a cat I had as a kid — but I haven't really articulated it like you did here. Gonna think about this one.