The user who asked this question has offered the bounty worth 500 but their own reputation is just 314. Is it possible to offer a bounty worth more than one's own reputation?
As soon as you put a bounty on a question the reputation is deducted from your total - as there are no refunds on bounties. As such the resulting "lower than posted" rep means they originally had around 800 rep prior to posting the bounty.
No they can't offer more bounty then they currently hold but bounty is immediately subtracted when offered. If a user has 100 reputation and they offer a +50 bounty their rep immediately decreases to +50 reputation.