Unfortunately, there is very little that can be done about a bounty setter who has abandoned their bounty. Note that the bounty setter is notified via the site notification system, and email, if possible, that their bounty is about to expire. Beyond that there is a fail-safe, of sorts.
First, the bounty period does not end at the end of the bounty period (huh?) but instead is automatically extended by 24 hours, a so-called grace period during which the bounty setter can still manually award the bounty. If, at the end of the grace period, the bounty setter still hasn't manually awarded the bounty then we get into possible "automatic awarding".
- If the bounty setter accepted an answer that was posted after the bounty was set, that answer is awarded with the bounty.
Otherwise half of the bounty is awarded to the highest scored eligible answer, where an answer is eligible if it
- was posted after the bounty was set;
- has a score of at least +2; and
- was posted by a user other that the bounty setter.
If two or more answers fit all the criteria, the half-bounty will be awarded to the answer that was posted first.
(This, and more, information about the bounty system, can be found in the Meta Stack Exchange bounty faq.)