Supposedly, sharing the quest with another character can get you the reward if you missed it the first time, though i'm not sure if that allows to pick up the item itself.
I say "supposedly", since we've seen numerous reports of people being stuck, even on a second shot (Anya quest comes to mind, especially).
On the other hand, there's a tricky way to bypass item destruction upon quest completion.
It's quite a funny thing to still have the item, while not being able to pick it up anymore if you drop it =]