DU,
I don't think the priests are obliged to 'absolve' them, particularly when it comes to the most serious crimes. And maybe a good priest would advise the offender to give themselves up. If such people have taken the step of going to the confessional, it does indicate some kind of moral conscience. I doubt that a murderous psychopath would give a monkey's toss.
It may indicate a moral conscience, but the problem (or rather one of them) is that a ne'er-do-well could see doing penance in the confessional as sufficient to atone for his crimes and so not trouble with the really rather disobliging business of police, courts, prison etc. After all, if a priest tells him he's now right with god why bother with the rest?
There was incidentally a nuanced and articulate priest here (or possibly on the old BBC mb) a while back who said that, even if someone in the confessional told him that he'd put a bomb in a primary school and wouldn't tell the cops still the priest wouldn't shop him to the cops. That seemed to me - and still seems to me - to be an example of the utterly morally corrupting effect that thinking there to be a higher authority can have.