Yep, this is how it's supposed to work. See the privilege page for bounties:
Bounties expire after seven days. You will receive several notifications a few days before this happens.
If you do not award the bounty within 24 hours of the bounty period ending, half the bounty value will be automatically awarded to the top voted answer posted after the bounty start, provided it has a score of at least 2. If no new answer matches this requirement, no reputation will be awarded at all, and the reputation used on the bounty will be lost forever.
Please note that once a bounty is started, the reputation is non-refundable under any circumstances.
What you're really 'buying' with a bounty is attention to your question, not a guarantee to get an answer. In some cases this bites, but it's essential to keep people from gaming the system. See How does the bounty system work? for more information.