Q. I know that the Torah says that one must not stand idly by when another person’s life is in jeopardy. What if the other person says, “Go away and let me die”?
A. Saving a life will always come at a price. According to Jewish law you must be prepared to suffer inconvenience and even pain in order to perform the mitzvah. Some views add that you must even be prepared to lay down your own life, but not every authority agrees (BM 62a).
If, however, the other person tells you not to try to save him, you are not obligated to take heed of the request. You have a duty according to the Torah to preserve human life, even if the other person says, “l don’t want my life saved”.
What they are telling you is that they want to commit suicide, and neither they nor you are entitled to decide that suicide is the right option (Maimonides, Hil’chot Rotze’ach 1:4). Life is given by God, and the only one who can decide to end a life is God Himself.