I twice left a bag on the NYC subway. Both times, an expensive-looking leather bag containing mostly work papers, some items with my address and personal items (no wallet or credit cards, thankfully). I filled out a claim form, but never gonna see that again, right? Well, not the first time, but the second time, about two months after losing it, I got a postcard from the MTA telling me it was at the Lost & Found. Miracles happen! (I remember it contained a library book, which I was very glad to return. It would have been way overdue, but I'd renewed it a few times in the naive hope it would turn up or that the finder might return it.)
Years ago I also left a briefcase on a bus, which I realized about 30 seconds later, so I started chasing the bus, first on foot, then in a taxi. When I caught up to the bus, a woman sitting in the back was holding it. When I said it was mine she turned it over without a word. Later, I found several personal items inside it, apparently belonging to the finder.