Because people from far away are less likely to imagine ever needing an Oyster again, yet might still need one right now (especially before contactless payment cards would work just as well for most short term visitors) there was a scheme where you could just "donate" your card to charity at places like airports, I don't know if it still exists.
Because Oyster is variable fare even in the simplest scenarios (a trip from Stockwell to Brixton for example, versus a train going from central London out to Amersham at the far end of the line are different prices, before any consideration about season tickets, time of day etc.) it is possible to have a card that's valid to enter the system (it has enough money that you could make some trip) but then make a trip it can't pay for. In this case the balance on the card falls below zero on exit, to use it again you'll need to first pay the excess and enough for a ride somewhere. So you'd expect to see some number of cards discarded in this state, since they are in some sense less than worthless. But the inconvenience of needing a new card seems to out-weigh that.