What is the meaning of the famous words "Wanted Dead Or Alive"? Did they mean that it was for some reason legal for ordinary people to kill the fugitive described on the poster? Is there still this power in the world, for someone to declare that other people may legally be killed?
In the USA, people acting as Bounty Hunters have been (and in some cases still are today) legally allowed to arrest fugitives who have a valid warrant out for their arrest.
If said fugitive uses deadly force to evade or deter capture, of course the arresting parties are perfectly legally allowed to defend themselves (also with deadly force). But historically (until 1985!) you could shoot someone merely for trying to evade capture.
Technically this doesn't allow you just flat out murder a sleeping person. But once they are dead, they can't exactly dispute your version of events either. If they were wanted for a bad enough crime, law enforcement probably isn't going to be too inclined to get picky.
The exact details of the modern situation are probably better asked on a Law or Politics stack. But I did touch above on it being not quite as extreme now, but still in some situations quite possible for a private citizen to make a living as a bounty hunter in the USA.