To preface, I disagree with the death penalty in most cases.

It may seem a strange idea, but as long as the death penalty is a thing, I wonder if there is an opportunity to instead of killing the person, provide the option (after serving a sufficient term for 'punishment' and/or 'rehabilitation') of instead killing the person's citizenship; as an alternative, if they have dual citizenship, allow the other country the option to take their citizen back in, drop their US citizenship, and permanently make them ineligible from regaining citizenship; and in cases of only US citizenship (because you aren't allowed to make someone 'stateless'), allow another nation to sponsor the individual by granting them citizenship (should the person accept) and taking them in.

The other country in such a case would be responsible for whatever further 'punishment'/'rehabilitation' they feel is appropriate before re-integrating them into society. There's only a couple thousand death row inmates in the US currently.

I'm not saying other nations will be jumping to take in murderers, but with the high number of false convictions in the US, and risk of executing innocent people, some nations with a high moral standard, may be willing to take some people in if given the opportunity.

Just a random thought that occurred; if it is extremely crazy sounding, I don't know. But the US is basically a prison nation with plenty of innocent people being convicted of crimes all the time, it may be nice for there to be another option.

Edit: Treason, and crimes against the nation, is one of those things that probably shouldn't be allowed such an exception, because you are just sending someone who 'committed treason' to a place they can continue to act against your nation, that's just not a smart thing to do.