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לא תעמוד על דם רעך

(ח) [ח] ומנין שאם אתה יודע לו עדות שאין אתה רשאי לשתוק עליו? תלמוד לומר "לא תעמוד על דם רעך". ומנין אם ראית טובע בנהר או לסטים באים עליו או חיה רעה באה עליו, חייב אתה להצילו בנפשו? תלמוד לומר "לא תעמוד על דם רעך". ומנין לרודף אחר חבירו להורגו, ואחר הזכור, ואחר נערה המאורסה חייב אתה להצילו בנפשו? תלמוד לומר "לא תעמוד על דם רעך". "ולא תשנא את אחיך" – יכול לא תקללנו, לא תכנו, ולא תסטרנו? תלמוד לומר "בלבבך" – לא אמרתי כי אם בשנאה שבלב. ומנין שאם הוכחתו ארבעה וחמשה פעמים חזור והוכיח? תלמוד לומר "הוכח תוכיח". יכול אפילו אתה מוכיחו ופניו משתנות? תלמוד לומר "ולא תשא עליו חטא".

(8) 8) And whence is it derived that if you can testify on someone's behalf, you are not permitted to remain silent? From "You shall not stand by the blood of your neighbor." And whence is it derived that if you see someone drowning in the river or being waylaid by robbers or attacked by a wild beast, that you must rescue him? From "You shall not stand by the blood of your neighbor." And whence is it derived that (if you see) a man pursuing another to kill him or to sodomize him, or after a betrothed maiden, that you must rescue the pursued by (taking) the life of the pursuer? From "You shall not stand by the blood of your neighbor." (19:17) "You shall not hate your brother in your heart. Reprove shall you reprove your neighbor, but do not bear sin because of him.") "You shall not hate your brother": I might think (that this means) that he should not curse him or strike him or slap him; it is, therefore, written "in your heart." Scripture speaks only of hatred in the heart. And whence is it derived that if he reproved him four or five times (and he did not take heed), he should keep on doing so? From "Reprove shall you reprove." I might think that he must do so even if his face changes color (in shame); it is, therefore, written "but do not bear sin because of him."

מתני׳ ואלו הן שמצילין אותן בנפשן הרודף אחר חבירו להרגו ואחר הזכר ואחר הנערה המאורסה אבל הרודף אחר בהמה והמחלל את השבת ועובד עבודת כוכבים אין מצילין אותן בנפשן:
MISHNA: And these are the ones who are saved from transgressing even at the cost of their lives; that is to say, these people may be killed so that they do not perform a transgression: One who pursues another to kill him, or pursues a male to sodomize him, or pursues a betrothed young woman to rape her. But with regard to one who pursues an animal to sodomize it, or one who seeks to desecrate Shabbat, or one who is going to engage in idol worship, they are not saved at the cost of their lives. Rather, they are forewarned not to transgress, and if they proceed to transgress after having been forewarned, they are brought to trial, and if they are found guilty, they are executed.
(א) אִם־בַּמַּחְתֶּ֛רֶת יִמָּצֵ֥א הַגַּנָּ֖ב וְהֻכָּ֣ה וָמֵ֑ת אֵ֥ין ל֖וֹ דָּמִֽים׃
(1) If the thief is seized while tunneling, and he is beaten to death, there is no bloodguilt in his case.

גמ׳ אמר רבא מאי טעמא דמחתרת חזקה אין אדם מעמיד עצמו על ממונו והאי מימר אמר אי אזילנא קאי לאפאי ולא שביק לי ואי קאי לאפאי קטילנא ליה והתורה אמרה אם בא להורגך השכם להורגו

GEMARA: Rava says: What is the reason for this halakha concerning a burglar who breaks into a house? He explains: There is a presumption that a person does not restrain himself when faced with losing his money, and therefore this burglar must have said to himself: If I go in and the owner sees me, he will rise against me and not allow me to steal from him, and if he rises against me, I will kill him. And the Torah stated a principle: If someone comes to kill you, rise and kill him first.

https://mida.org.il/2016/06/28/%D7%A2%D7%93%D7%95%D7%AA-%D7%94%D7%9E%D7%A4-%D7%9C%D7%90-%D7%9E%D7%95%D7%AA%D7%99%D7%A8%D7%94-%D7%A1%D7%A4%D7%A7-%D7%90%D7%9C%D7%90%D7%95%D7%A8-%D7%90%D7%96%D7%A8%D7%99%D7%94-%D7%96%D7%9B%D7%90/