Recently I set a bounty on a superuser question. Unfortunately I was very very busy for the next week and only logged in once or twice on SO. Now the problem is, the bounty on superuser expired unnoticed. Wouldn't it be a good idea if a user is notified if a bounty expires even if he is visiting another SE site?
Well, your email must be invalid or misconfigured; there are always email notifications of expiring bounties before they happen.
I just checked your account here and on SU... and sure enough, no email.
So the "fix" for this "bug" is to provide a valid email address in your account. Then use the "copy profile to all sites" button to make sure it propagates everywhere in the network.