I won't go into the topic at length only to say that someone immigrating here who commits a crime here, is different than someone who committed a crime in their home country and then coming here. The topic of what an appropriate punishment is depends on whether the individual is the former or the latter. As cold as it sounds, there is also a cost/benefit analysis to do: if they're more a detriment to the host country than they're worth, and they're a criminal in either case (whether they stay or are sent back), then it's clear they shouldn't have been in the host country to start with. Whether they are deserving of death depends on the crime, the culture (the "way of their people" as it were), and a host of other factors. Above all, was the crime reprehensible (murder, rape, cannibalism, massive fraud on society, etc, etc?). I think this comes down to asylum laws, which are a matter to be decided on a nation by nation basis. Very thought provoking question.