This is a question that makes a lot of people very uncomfortable because the honest answer requires you to separate your emotions from your logic and , that is absolutely not always easy to do especially when we are talking about people who have committed terrible things.

But let me share my thoughts anyway.
I think inmates should have access to healthcare, And before you close your mind on this post let me explain why I am saying that because it is not as simple as feeling sorry for criminals or thinking that what they did does not matter.
First let us establish something, the moment a person enters the prison system they are under the complete control of the state, they cannot go outside to see a doctor, they cannot take care of themselves the way a free person can, they cannot make independent decisions about their own health and wellbeing, everything about their existence is controlled by the government, and if the government is going to take that level of control over a human being then the government also takes on the responsibility of keeping that human being alive and in reasonable health,You cannot have one without the other.
Now the tax argument, I understand why it bothers people alot , you are working hard and paying your taxes, you struggling to afford your own healthcare, and then you now hear that the same money is going toward someone who committed a terrible crime, that feeling is very valid, I am not going to tell you that it is not, it is genuinely frustrating really.
But let me ask you something, what is the alternative then? If we deny sick inmates healthcare and let them suffer or die in prison? Because that starts to sound less like justice and more like cruelty, and once a society decides that cruelty is acceptable for certain categories of people it becomes very difficult to draw the line at exactly where that cruelty stops, today it is violent criminals, tomorrow the definition of who deserves basic care starts shifting and shifting until it includes people it was never supposed to include.
There is also a very practical argument here that people overlook, prisons are enclosed environments, diseases do not check a persons criminal record before spreading, so If inmates are denied proper healthcare and infections go untreated, outbreaks happen, those outbreaks do not stay neatly inside the prison walls, prison staff go home to their families, people get released, the public health consequences of completely neglecting inmate healthcare are real and they affect law abiding citizens directly.
And then there is the matter of rehabilitation, not every person in prison is there forever, a significant number of inmates will eventually be released back into society, what kind of person do you want walking out of that prison? someone whose health was completely neglected for years, who is sick, broken, and bitter? or someone who was treated with at least the basic level of human dignity and has a fighting chance at functioning in the world again? The answer to that question affects everyone not just the inmate.
None of this means that criminals should live better than free citizens. None of this means there should be no consequences for terrible actions, prison itself is the consequence, the loss of freedom is the consequence, basic healthcare is not a reward, it is just the minimum standard of human treatment that a functioning society should be able to maintain even for its worst members.
Because how we treat the people at the very bottom of our society says everything about the kind of society we actually are.
Not the kind we claim to be, the kind we actually are.
Think about that.
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Exactly.
The more we think of it as prison, the more we feel those in there don't deserve care. But as a rehabilitation center, we start seeing the more reason why their needs should be catered for.