We lost a cat a few months ago. She's been an indoor/outdoor kitty for quite some time, and we've seen her hopping the fence into the neighbor's yard, but as far as we knew she'd never spent a night outside.
At some point we realized we hadn't seen her in a couple days. Then a couple days stretched toward a week and we started to worry.
We did all these things--call the "shelters", put up flyers, etc. No bites on any of them. At some point we gave her up as lost. She was the troublemaker in our household pet ecosystem, and while we love her, having her not around actually made for a more peaceful home. So it was not with compete grief that we gave her up as lost.
Then, about two weeks after she vanished, she showed up at the back door one day. She'd lost weight (and made a beeline for her food bowl), but otherwise seemed fine. My suspicion is that she got trapped somewhere--somebody accidentally closed her in a shed or something--and couldn't get home. Because she clearly knew where home was, and came back when she wanted to bad enough. She's now stalking the house, bossing all the other animals around as if she never went anywhere.
The only "hit" we got from all our efforts was, somebody called to say they'd seen her a couple streets over... while I was looking at her in my living room. She'd been home for several days at that point.
I hope your story has a similar happy ending.