Strong point. My first thought is that foreign countries probably won't take a proven murderer or rapist in the first place, in which case he would be forced to choose between execution, prison, or abandonment far enough from society that he could never return.
I had in mind that this could be used more for controversial cases in which one country's government may believe the person is innocent or should be spared for whatever reason. It would be up to other countries whether to and how to take in certain people. One country may offer a life sentence with some job he has to work in the prison to subsidize his stay. Another may offer freedom on probation of some king. Another may not take him at all. If someone has access to classified documents by virtue of position and commits espionage by leaking them like Edward Snowden did, he could cause no future harm if he has no access to future documents, so a country may be willing to take him but ban him from high-risk positions.
The reason I suggest this isn't because I believe that murders or rapists should be granted a second chance. I ask because I don't trust the government with the power over its citizens' lives. What if a puppet congress of a dictator declares that dissent toward military actions is treasonous and make an example by executing people who speak out against them at all during war?