For the most dangerous of criminals, an escape, such as with 'El Chapo' Guzman, could mean the death of many citizens, be it civilian or law enforcement. The criminals who pose the highest risk should be executed as the lives of the many should outweigh the lives of the few.
Psychopaths who commit terrible crimes do not deserve to remain on earth. They have no prospect for reform and will only corrupt other prisoners and letting them remain in jail is a waste of public money. If there is no doubt they did it, just shoot them (very cost effective).
perhaps the issue is justice, not punishment. A criminal sentence may serve to approximate a just outcome for the victims, the perpetrator and for society in general. A death sentence, capital punishment, may be the closest approximation to justice for some crimes.