There`s a lost baggage or baggage services office (which you`ll know about if you`ve ever had an airline lose your luggage-) that eventually collects unclaimed bags from the carousels or whatever. They must then enter it into some kind of tracking database, knowing what flight it arrived on and with the data from those baggage handling tags the check-in agents attach, which are barcoded. Somehow that`s how most owners must eventually be re-united with their bags.
I`ve read about permanently [orphaned" bags that never get returned - not sure what happens to them or how that even happens in the age of universally required ID to fly. But if you fly thru any large airports, you`ll see airport personnel removing bags & putting them aside from carousels where bags from a newly arrived flight are getting ready to come out and the bags from a prior flight are just going `round with nobody grabbing them. They`ll just set them together there on the floor nearby for awhile so owners can see them & get them, and whatever`s leftover even after that, if anything, eventually make their way back to that services office I mentioned.