I think, should you choose, you should be able to return award reputation you obtained from a bounty, possibility in the first week. Why? (Well, why not?)
I would like this feature as I recently answered a question that had no answers around 6 days left. The author of the post (who did not own the bounty) gave me the accepted answer maybe 4-5 days left. With less than 24 hours to go (I think 5) another answer was posted.
I obtained the bounty, but I feel neither my answer, nor the other answer, were really the best possibly answers. While my answer was 'accurate', I was secretly hoping that someone who knew more about it than me would post. As such I can accept being 'accepted answer' as I answered the question, but as far as a bounty I don't feel it was informative enough.
There's probably reasons not to do this, but I figure if it was purely at the discretion of the person awarded the bounty it couldn't 'hurt'.
EDIT: As mentioned by droid you could answer your own question on another account and then send it back (thus getting answers, and maybe even easy attention for views / reputation). So I figured maybe require reputation to send it back (I was thinking same as setting a bounty (75), NOT counting bounty awarded). With this friends could still cheat the system, but if it was done often would seem easy to catch.