It follows then the person that kills a death row inmate is responsible for their death, not the inmate for committing a crime in the first place.
Anyway, it's not interesting, the only thing the parents are responsible for is having a second child and breaking the law. What people do to enforce the law is their responsibility not the responsibility of the parents that broke it, the same applies for the murderer on death row.
Just because something is legal doesn't absolve you of responsibility. The same way soldiers "just following orders" are responsible for the actions they commit at the behest of their superiors. Both the superiors and the soldiers are responsible
The criminal is only responsible for breaking the law, the only thing he had control over before he was caught (assuming he was caught for the sake of argument). We as society are responsible for dealing out the punishment.
How could the criminal be responsible for the punishment when he is not the one inflicting it on him/herself.
edit: To make my argument slightly easier to understand I'm going to give an extreme example
Let's say it's illegal to be a certain religion. Is it the insert religion here person's responsibility that he is punished and sent to a death camp?
Your "need" to kill them because they crossed some line is your need, and you're the killer. (For better or worse...)
It's really similar to jumping out of the 10th floor window. It's the dv/dt that actually kills you, but it's you who is responsible for your own death.