LOST AND FOUND BIKES
There's this saying on playa that there's no such thing as a lost bike until after the event is over. And while that sometimes ruffles people's feathers who are looking for their lost (or misplaced) bike, it's unfortunately true.
See, people leave their bikes around all the time, and may eventually come back to them. It doesn't mean they're lost. Or somebody accidentally (or not so accidentally) borrows a bike they see laying around (we call this stealing), uses it, and then either brings it back (unlikely) or abandons it somewhere (more likely). How can you tell that bike is really lost? Right, you can't.
So it's nearly impossible at any given moment during the event to determine what might have happened to a particular bike, and so it's pretty futile to assume anything until the proverbial dust settles.
At the end of the event, lost bikes (e.g. abandoned ones that have been gathered up) can be recovered at the Yellow Bike Camp. Post event, you can write lostbikes(at)burningman(dot)com. Eventually, unclaimed bikes are donated to Reno-based non-profits that fix them up and provide them to underprivileged kids.
That said, DO NOT ABANDON YOUR BIKE ON PLAYA. Leave No Trace, people. Take it home with you, just like you take everything else you've brought.