When you offer a bounty of, say, $50$ on some question to get it more focused, that many reputations get deducted from your acquired reputation. $50$ being the minimum reputation for offering bounty, how can a person offer a bounty whose reputation is less than $50$? I have seen many posts like that.
The privilege to set bounties is granted at 75 reputation, so it is actually impossible for a user with less than 50 reputation to set a bounty. (Note, too, that if a user once had enough reputation for a privilege but somehow loses reputation to fall below the threshold, the privilege is revoked.)
But the reputation offered in a bounty is removed from the setter's account as soon as the bounty is set, not when it is awarded; from the privilege page linked above (some emphasis added):
What happens when I place a bounty?
The reputation you're using for the bounty is immediately and irreversibly deducted from your reputation.
So, for example, if a user with 80 reputation sets a 50 reputation bounty on a question, those 50 reputation points are removed from their account at that time, and it looks as though a user with only 30 reputation has set the bounty.