Here is a discussion on the Amazon Customer Discussion boards about how ebooks from Overdrive expire on the Kindle.
It seems that if the wireless is shutoff on the Kindle there is no mechanism to expire the book from the device. This allows people that need more time to finish a library book to keep their wireless off so that the book does not expire and they can continue to read the book even though technically it is due.
On the discussion board there seems to be some debate about whether this practice holds up other users that want to use the book. From reading over the thread I think it is the case that the book goes to the next person in line even though the book is still on the other persons Kindle. The library system shows the book as expired so it goes to the next person.
There is probably one person out there that made an investment in a "library" Kindle. You buy a Kindle for $79 and you never turn on the wireless. You then load library books on the Kindle via USB and the books never expire.
Several years ago there was news stories about a new DVD technology that allowed for DVDs to degrade when exposed to air. The idea was that you could have a rental DVD that you did not need to return because 48 or 72 hours after the DVD was first opened and exposed to air in would no longer work. From the articles the degradation process was based on oxidation and this made the disc unplayable. The idea never took off mainly because of environmental concerns. Every rental under this model would become trash after a couple days. A friend and I joked that if these DVDs had taken off there would be some geeks somewhere that would build an argon chamber to store their rental DVDs in so that they would never oxidize. We joked that someone would build a $20,000 airless chamber to save $500 on DVD purchases.