If there is no way to help the person who is ill , no matter how much effort and attempts, then we would have no choice if the illness is severe or terminal. Letting them live would bring more pain to their life. By putting others out of their misery, we can no longer feel our pain. Sure, we don't want to die, but sometimes we have no choice.
I feel that it should never be okay to take someone else's life, it should always be that person's choice to take their own life instead of someone else doing it for them. You should never kill someone else, always let them do it because then everyone would feel "does he want to put me out of my misery?" Even when they might feel fine