When a user offers a bounty and if the question did not got any response or the question has been answered by himself then the the reputation for the bounty will be not awarded to anyone. So I got this idea of how about following Law of conservation of Reputation (Enegry of SO). I wanted to hear some suggestions on this.
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Consider the bounty as payment for giving the question more attention. When you drive a car, you don't get the fuel back, right? Yet energy is conserved--converted into a different form. Here, the "energy" (rep) is converted into a "different form" (attention).
The intended functionality of a bounty is to give the question extra attention (also to entice users to take extra time and write more detailed answers). You pay for the attention with the rep--you can't recover it if it doesn't pay off. Touching on cars again, you don't get the fuel back if you took the wrong road and got lost (thus wasting fuel with no gain from it).
Stealing @Dave's analogy (unfortunately not energy-related) from the comments:
Another issue with refunding bounties is this:
Lots of people will just never revoke the bounty (i.e., keep re-applying it), and the featured tab will get cluttered. Eventually, it will become like the Unanswered tab--full of lots of questions of which a small percentage get answered. The only difference is that there's an extra rep gain, so people will like using this "new unanswered tab" better.
So, placing a bounty will make it get lost within the featured tab. Of course, you could sort the tab by "newest"--but that's extremely unfair to users who use bounties to get attention/answers for their old, unanswered posts (one of the primary uses for bounties, in fact). If they sort it by posts that have recently been bountied, the re-bountied posts will come up. Yes, you can come up with a "been bountied only once/etc" metric, but that just gets complicated.
Also note that there already is something to make re-bountying harder (the re-bounty must be higher than the previous one). Now, there's probably a reason for it-- if the post didn't get an answer, it's probably not worth the previous bounty . This feature request works against the spirit of the existing feature.
Consider the consequences of this change, though...
If fruitless bounties were refunded, having a "featured question" essentially becomes free of charge. The charge only applies when a suitable answer is provided. Thus, people could (and very likely would) leave their bounties up indefinitely.
This would clutter the featured questions. The list would grow in lock-step with the total questions for the site and would very quickly create a higher noise-to-signal ratio. This would devalue the purpose of the bounty in the first place, as offering a bounty would just get lost in a vast sea of other bounties, with very little difference between the featured questions and the regular questions.
The price is for the advertisement, not for the result. Results may vary.