Some funny comments on here, odd cats, and a few odd humans too. No point generalising about cats, huge differences in habits and temperament, we've had all sorts, the latest is fairly ancient, has been outside but clearly isn't overly interested in the outside world, and though deaf is exceptionally sensitive. Others we've had have been largely outdoor cats, noisy, or quiet, stroppy, or so laid back as to be almost horizontal.
We did have one who adopted us, after several months we discovered she was from the next road, took her back, within a couple of days she was back - for good. Presently we get visited by a cat from over the back, but we realise he mostly turns up when there's a lot of children noise, and he prefers peace and quiet. So, don't bother making stereotypes.
The OP story, about a cat who moved house, sadly some folk don't realise that their sweety-pie cat may just leave home? I knew a couple, they both worked, had no idea their loving cat actually spent weekdays at an old couple who were neighbours, snoozing on their sofa or watching the telly. Then at teatime it snuck back 'home' for when they got back. For years they didn't realise they were sharing a cat, until a chance meeting and conversation.