My players have become entangled in a murder mystery in 1748 Prussia (using the Götterdämmerung system), and are trying to work out who the killer is while trying to both stay alive and avoid suspicion being directed their way. The outcome of this quest is rather open since they could basically give up and just run for the hills at any second (with the risk of being blamed for the murders).
Everything is set up in such a way that if the players can get the killer arrested by the authorities, they will be rewarded with an amount of money and an improved standing with the local law enforcement.
Problems arise if the players should take the law in their own hands and go after the killer in the pursuit of revenge. A monetary reward is not suitable should they find and kill the criminal, since their vigilante justice is pretty much murder in its own right. A simple skill point reward is always given on the completion of a "chapter" in my campaign and increasing such a reward is not appropriate either.
How should I reward my players for completing a quest in a way it was not supposed to be completed? Is it simply a failed quest since the optimal target was to make the killer face justice in court, or is the vigilante way just another way to completion?