"Let them die" is acceptable - it's called suicide.
"Kill them in mercy" is not - you can not make such a decision for another person, ESPECIALLY on ground that might be terryfing to you (isolation) but are evidently not to everyone (hermites do it out of their own free will).
If we are talking about immense pain and inevitable death, then we can discuss - but even under these circumstances, if the individual is able to communicate, the decision MUST be its own.
But let's look at it objectively, that human beings are social creatures, and those who cannot function around others, are inherently broken--the mere absence of others does not merely cause observed psychosis in sustained confinement, like on Japan's death row, but is shown to do so in other primates and causes permanent mental dysfunction. I can go through and find and cite studies if you want, though I believe the principles are generally well-established. The human psyche is simply adapted to having people around. Furthermore we can all agree that sustained, forced isolation is a cruel and unusual punishment when it's involuntary.
"mental dysfuntions" are irrelevant. A lot of people have mental disfunctions and can live their lives - and be happy with them.
In order to mean anything, you must show that these mental dysfunctions make living unbearable, due to immense pain (pyschological pain/"discomfort" included).
The issue at hand was the suggesting that we let prisoners who would have to be put into total isolation, modern US "Supermax" conditions due to their violence, instead choose to die... The problem being that if we put them into those conditions, how can they make any kind of choice at all? We're torturing them until they've been driven mad by doing so. We cannot put anyone in those circumstances to begin with who is sane.
How is that a problem? It is not as if we render them mute.
A lot of people have a problem with the possiblity that a person might WANT to die - suicide is normally seen as an irrational, spontaneus act. This is of course true in most cases, but there are also circumstances where it is a rational, well-considered choice. This would be such a circumstance.
It does not even require that anyone kills the prisoner - you merely have to provide the means. Heck, make it an official possibiltiy - i can not consider anything wrong with it, as long as enough checks and balances are in place.
And that is the key qualifier. Someone whose brain is sufficiently altered in function from baseline humanity as to find human companionship unnecessary, should not be in a prison or on death row. We have places called mental hospitals for those individuals.
Well, yes and no. There are propably a lot of individuals that would profit from such treatment - we might not be able to ever release them, but it might improve their lives.
On the other hand, a lot of serial killers
are beyond hope. Putting them into a mental hospital would not only be a waste of resources - and propably even a form of torture (it has been done in the GDP, at least partially by psychatrists who really meant well.)
Fazit:
I opppose the death penatly. Of course, that means that we must do something else with these people.
The first option should be a closed, mental facility, IF we can be reasonably sure that it is not too dangerous for the personell.
The second step (since it is unlikely that a lot of them can be rehabilitated) should be isolation.
We are talking about people (such as serial killers) who already lack attachemnt to other people - being isolated will not harm them as much as a normal person.
On the issue of suicide (of the prisoners): It is a human right to decide about ones own body. This includes the decison to die. There is no reason to deny them this right (expect revenge-driven hate). Therefore, we should not deny them this right.
However, proposing a "mercy kill" can NOT be justified - this would be a death penalty by another name, and even worse, since you do not justify it with their crimes but rather with their personality.