Depressed Child

If a parents child was constantly miserable... Like, unreasonably and ultimately depressed, every day of their life, from 4 years old until 25, and they died, would that parent feel relief, like a chronic cancer patient dying, or would they feel upset for the rest of their life?

Unless a person has gone through it we can only tell you what we think.

I would imagine, had the parent truly loved the child, they will feel terrible. And like other parents who have lost a child, never get over it. Though time takes away some of the rawness.
I would imagine too, at the same time, had that child been a source of constant negativity, and without let up, as your post suggest... I would think the parent, or a part of that parent, can't help but feel relieved to not have to deal with that anymore.
It would be a natural feeling and completely out of their control. And I would think they might feel guilty for feeling that way; which is understandable and natural too. But they really should not.
Having negativity flee one's life is a good thing, regardless 'how' it goes.

Having recently faced something similar (not with a child though) there is indeed a great deal of emotions and feelings involved, same with any grief process and yes if the person that ultimately died did suffer from depression, and/or an illness that affected their ability to live their life then relief is something that would be felt by the surviving person. Along with that relief also comes guilt for feeling that way.

We hate to see people suffering (normal well adjusted people do) and if we are unable to help them it makes that all the more harder so in some when when that suffering ends we can't but help having a sense of relief that the person is no longer suffering but also our suffering ends as well, kinda, although you have the grief suffering to deal with in the aftermath.

Entirely depends upon the parent. Feelings have to be shared to be understood. If the child can't or won't spread that misery then so what?

I was a moody child but was encouraged to mask my feelings. My parents signaled early that emotions were untrustworthy.

Death can be a friend if misery is that severe. Medicine both theoretical and practical likely ought to have a say.

My question would be did the parents know or even do anything about the child's depression? Depending on the answer to that would I feel depend on how they would feel after the child's passing!

Said child has been through therapy since they were 4, seen over a dozen psychs and therapists, been in and out of counseling and inpatient facilities, and tried over 15 different medications, none of which worked in the slightest.

In that case I suspect that there would be somewhat of a mixed reaction. They may be somewhat relieved that the child is no longer suffering (not sure if that's the right term for it or not) BUT would be very sad that they had lost the child. They may well feel that they have failed in trying to care for the child & find a solution. People deal with grief in many different ways, it would be very difficult to speculate as to there feelings on this.