Death of Tzadik Atones

 Torah Temima (Vayikra 16:1.1): The Yerushalmi states that just as Yom Kippur atones for the Jewish people so does the death of tzadikim. This gemora does not explain the significance or the reason why the death of tzadikim atones for the Jewish people. It appears that an answer can be found in Pirkei DeRabbi Eliezer (Chapter 17) concerning the death of Shaul. In Shmuel it mentioned that the bones of Shaul were buried. This indicates that when G d saw how they cried and mourned for Shaul that this aroused the attribute of Mercy. We see then that it is not the death per se of the tzadik that brings about atonement but rather the honor and mourning for the tzadik, because the honor of the tzadik is in fact the honor of G d.

Shela (Tanis Aseres HaDibros, Torah Ohr 4:44) This that it says in Moed Koton (28a) that just as Yom Kippur atones so does the death of tzadikim atone. In other words just as Yom Kippur does not atone without repentance so too the death of a tzadik only atones for those who repent. But  possibly it is teaching that both Yom Kippur and the death of a tzadik atone with and without repentance  but that is not so as we learned  from previously regarding the bones of Shaul. Thus we learn here that only with repentance does the death of a tzadik and Yom Kippur atone. This is reinforced by the statement : Why is the death of Miriam adjacent to the section of the Red Heifer in the Torah? Just as the red Heifer atones so does the death of tzadikim and that is only for those who repented. 

 Bamidbar Rabbah (19:08) A certain idolater asked Rabban Yoḥanan ben Zakai: ‘These actions that you perform seem to be a type of sorcery. You bring a heifer, burn it, crush it, and take its ashes. One of you becomes impure from a corpse, one sprinkles upon him two or three drops, and you say to him: You are purified.’ He said to him: ‘Has a spirit of insanity never entered you?’ He said to him: ‘No.’ ‘Have you seen a person into whom a spirit of insanity has entered?’ He said to him: ‘Yes.’ He said to him: ‘And what do you do to him?’ He said to him: ‘We bring roots, smoke them beneath him, and sprinkle water on it, and it flees.’ He said to him: ‘Let your ears hear what you express from your mouth. The same is true of this spirit, this spirit of impurity, as it is written: “I will remove the prophets and the spirit of impurity from the land” (Zechariah 13:2). We sprinkle upon it the water of sprinkling, and it flees.’After he left, his students said to him: ‘You rebuffed this one with a reed. What do you say to us?’ He said to them: ‘As you live, it is not the corpse that impurifies, and it is not the water that purifies. Rather, the Holy One blessed be He said: I instituted a statute, issued a decree; you are not permitted to violate My decree, as it is written: “This is the statute of the Torah.”’

Moed Koton (28a) Wherefore is the account of Miriam's death placed next to the laws of the red heifer? To inform you that even as the red heifer afforded atonement by the ritual use of its ashes, so does the death of tie righteous afford atonement for the living they have left behind.

Moed Koton (28a) Wherefore is the account of Aaron's death closely followed by the account of the disposal of the priestly vestments? To inform you that just as the priest's vestments were means to effect atonement so is the death of the righteousconducive to procuring atonement.

Vayikra Rabbah (20:12) Rabbi Abba bar Avina said: Why is the death of Miriam juxtaposed to the ashes of the heifer? It teaches that just as the ashes of the heifer atone, so the death of the righteous atones. Rabbi Yudan said: Why is the death of Aaron juxtaposed to the breaking of the tablets? It teaches that Aaron’s death was as difficult before the Holy One blessed be He as the breaking of the tablets. Rabbi Ḥiyya bar Abba said: On the first of Nisan, Aaron’s sons died. Why, then, does it mention their death on Yom Kippur? It teaches that just as Yom Kippur atones, so, too, the death of the righteous atones. From where is it derived that Yom Kippur atones? As it is stated: “For on this day he shall atone for you, to purify you”. From where is it derived that the death of the righteous atones? As it is written: “They buried the bones of Saul”, and it is written: “and God acceded to the entreaty of the land thereafter”. 

Berachos (62b) And He said to the Angel that destroyed the people, It is enough. R. Eleazar said: G-d said to the Angel: Take a great man among them, through whose death many sins can be expiated for them. At that time there died Abishai son of Zeruiah, who was singly equal in worth to the greater part of the Sanhedrin.