Two related, but not identical, questions come up here (all providing, of course, that “dead or alive” bounties were/Are real and not a Western movie cliché). First, how can a government set incentives for citizens to kill another citizen? I’d suppose this would violate a number of the fugitive’s constitutional rights, even if he’s suspected of the most horrible crimes (or were “dead or alive” bounties set only on fugitives already convicted to capital punishment)? And how was it possible to pay the reward to bounty hunters who actually killed the fugitive without having to try them for murder or whatever? Were there statutory defenses provided for that they could come up with in a murder trial, or were they simply pardoned using the chief executive’s powers?
As a WAG, there’s no saying that the bounty hunters were encouraged to kill thier quarrry, but that the law understood at the time that going after the bad guy may end up in a “life/death struggle”, and that retrieveing the bad guy was the end goal.
The government was not the one offering the bounty in most cases.
It was usually corporate entities: the railroads, the banks, the stagecoach/express companies, etc. – those were the usual victims of these bandits, and the ones who most wanted them caught. But they seldom said “Dead or Alive”. In fact, they often included in small print “for the arrest and conviction of”, which gave the company an excuse to not pay the capturer if the bandit was killed without a trial.
“Dead or Alive” was more common on wanted posters for people who had been previously convicted of a crime, and then escaped (which seems to have been fairly easy, based on the number of times it’s reported).