(16) Thus [Aaron] shall purge the Shrine of the uncleanness and transgression of the Israelites, whatever their sins; and he shall do the same for the Tent of Meeting, which abides with them in the midst of their uncleanness. (17) When he goes in to make expiation in the Shrine, nobody else shall be in the Tent of Meeting until he comes out. When he has made expiation for himself and his household, and for the whole congregation of Israel, (18) he shall go out to the altar that is before Adonai and purge it: he shall take some of the blood of the bull and of the goat and apply it to each of the horns of the altar; (19) and the rest of the blood he shall sprinkle on it with his finger seven times. Thus he shall cleanse it of the uncleanness of the Israelites and consecrate it. (20) When he has finished purging the Shrine, the Tent of Meeting, and the altar, the live goat shall be brought forward. (21) Aaron shall lay both his hands upon the head of the live goat and confess over it all the iniquities and transgressions of the Israelites, whatever their sins, putting them on the head of the goat; and it shall be sent off to the wilderness through a designated man. (22) Thus the goat shall carry on it all their iniquities to an inaccessible region; and the goat shall be set free in the wilderness.
(2) So will he do for the Tent of Assembly i.e., he will sprinkle seven times before the ark-cover and on the corners of the incense altar
What does the seventh sprinkle cause?
אמר ליה ההוא צדוקי לר' חנינא השתא ברי טמאים אתון דכתיב (איכה א, ט) טומאתה בשוליה אמר ליה תא חזי מה כתיב בהו (ויקרא טז, טז) השוכן אתם בתוך טומאתם אפילו בזמן שהן טמאין שכינה שרויה בינהן.
A certain Sadducee said to Rabbi Ḥanina: Now you are certainly impure, as it is written about the Jewish people: “Her impurity was in her skirts” (Lamentations 1:9), and the Divine Presence does not dwell upon the Jews when they are impure. Rabbi Ḥanina said to him: Come and see what is written about the Jewish people: “That dwells with them in the midst of their impurity” (Leviticus 16:16). This indicates that even when they are impure, the Divine Presence dwells among them.
(8) Jerusalem has greatly sinned, Therefore she is become a mockery. All who admired her despise her, For they have seen her disgraced; And she can only sigh And shrink back. (9) Her uncleanness clings to her skirts. She gave no thought to her future; She has sunk appallingly, With none to comfort her.— See, Adonai, my misery; How the enemy jeers!
(4) השכן אתם בתוך טמאתם— This implies that although they are unclean nevertheless the Shechinah dwells in their midst (Sifra, Acharei Mot, Chapter 4 5; Yoma 57a).
אמר רב חסדא אמר מר עוקבא כל המתפלל בע"ש ואומר ויכולו שני מלאכי השרת המלוין לו לאדם מניחין ידיהן על ראשו ואומרים לו (ישעיהו ו, ז) וסר עונך וחטאתך תכופר
Rav Ḥisda said that Mar Ukva said: One who prays on Shabbat evening and recites vaykhullu, the two ministering angels who accompany the person at all times place their hands on his head and say to him: “And your iniquity has passed, and your sin has been atoned” (Isaiah 6:7).