Everybody starts with rights, but if you kill someone, you essentially forfeit yours. It's this rights-with-responsibilities idea that forms the basis of all justice. What would you base your system on?
Then that means they are not rights but privileges. And also, I don't think it's wrong to kill a killer. So there are not two wrongs in the situation. Like you said, they forfiet everything when they commit murder. I don't see them as human any longer when they do the disgusting things they do.
Let's paint a picture. A man is living at the very edge of society, scraping survival as best he can. It's not his fault, he had a great job until the company he worked for went bust. Now he finds out that so many others are competing for the worst work. The bank forecloses on his house and he's on the streets, now what company will hire a bum from the street?
Now one night a woman walks past after a night out and her purse is stuffed with cash she doesn't really need and he hasn't eaten properly for a week. He threatens her with a broken bottle but she struggles, in the scuffle the bottle cuts her artery and she dies in minutes.
He never meant to kill her, he only wanted to survive, the police catch him, find him guilty of murder. Is he also going to face the death penalty along with the bastards who poisoned their grandmother to get their inheritance?