After the initial shooting, Carter has one bullet left in his shotgun, he makes it very clear while talking with Bird about it. He also says there are no bullets around, no way to get more.
Given a good chance to kill the hitman, Carter shoots this last bullet, but it just injures the hitman, leaving him alive. Then Carter gives the shotgun to Bird, saying she should shoot the hitman in self defense in case Carter's final assault will fail.
My question is what's the point in this, knowing the shotgun is useless and without bullets? Would have made much more sense to ask her to escape through the window while he's distracting the hitman and keeping him busy.
Any explanation, or just a huge plothole?