I lost my passport between security and the gate once (the security staff inexplicably moved it into a new tray, so when I picked up my stuff from my two trays I missed the passport in the third tray). Losing your passport at this point turns out to be very complicated, but I was lucky that they held up the whole plane while I ran back to security to fetch it.
They lost mine once and I basically have to found it myself. Eventually found someone throw the bag in an corner...