Fortunately the Help Center helps out:
How is a bounty awarded?
The bounty period lasts 7 days. Bounties must have a minimum duration of at least 1 day. After the bounty ends, there is a grace period of 24 hours to manually award the bounty. Simply click the bounty award icon next to each answer to permanently award your bounty to the answerer. (You cannot award a bounty to your own answer.)
If you do not award your bounty within 7 days (plus the grace period), the highest voted answer created after the bounty started with a minimum score of 2 will be awarded half the bounty amount (or the full amount, if the answer is also accepted). >If two or more eligible answers have the same score (their scores are tied), the oldest answer is chosen. If there's no answer meeting those criteria, no bounty is awarded to anyone.
If the bounty was started by the question owner, and the question owner accepts an answer posted during the bounty period, and the bounty expires without an explicit award then we assume the bounty owner liked the answer they accepted and award it the full bounty amount at the time of bounty expiration.
As a special bonus, any reputation you earn from being awarded a bounty is exempt from the daily reputation cap.
There has to be answer to award the bounty, in this particular case there aren't any answers, so no bounty can be rewarded. The messages you receive are the standard messages. You cannot select an answer, nor can the system. If the deleted answer hadn't been deleted, the negative score would have prevented from being selected by the system as it needs a 2+ vote for automatic rewarding.
Basically, you cannot do anything. You could consider removing (deleting) the question, this is a very particular / intermittent failure that is very difficult to troubleshoot. You might find the solution yourself one day!