As this question did not yield any answer as to why bounties which have failed to attract auto-awardable answers – i.e., answered by somebody who did not start the bounty, answered after the bounty has been started, two upvotes in the week after being posted – should not be spared from expiration under certain conditions, I propose the following:
If a bounty’s grace period is about to expire without any answer being awarded that bounty automatically or manually, extend it until n days after an answer has become auto-awardable (e.g., with n = 7). Essentially treat the bounty as expired except that if an auto-awardable answer is posted, it can be automatically or manually awarded the bounty. Some suggestion on how to handle the details:
- The bounty can be awarded manually at any time.
- The question will not be listed on the featured questions anymore and thus not receive any additional exposure.
- The bounty does not count towards the per-user bounty limit anymore.
- The question loses the special protection against closure, which bountied questions have.
- Requiring two upvotes in the first week and not just in general avoids the bounty being awarded to answers that are bad but attract an upvote evry now and then.
- Unless the question has received an answer in the last n days, a new bounty can be started on that question, in which case the old bounty expires instantly. Note that without that restriction, one could start a bounty to deny an answerer the old bounty. Adding up bounties in this case has already been discussed here.
- I chose the end of the grace period to depend on the time of the answer becoming auto-awardable in contrast to the time the answer was posted to avoid instant auto-awarding after an upvote. This could be replaced by a more complicated system (in which, e.g., the grace period ends if at least n days have passed after the first auto-awardable answer has been posted and at least one day has passed after the first answer has become auto-awardable).
- I have no suggestion as to whether the bounty should still be indicated next to the question. In my opinion it does not cause much exposure as the question will likely vanish from the front page and thus this indication is only seen if the question turns up in searches and similar.
This way questions, on which an unsuccessful bounty was placed, retain at least some incentive for answers and thus the bounty starter has an at least a slightly increased chance to get something for the invested reputation. Also, somebody who missed the bounty period for whatever reason and can answer that question cat still get an extra award for helping the bounty placer (and answering what is likely a difficult question).