Commentaire sur Le Lévitique 16:16

מטמאת בני ישראל [AND HE SHALL MAKE AN EXPIATION FOR THE HOLY PLACE] BECAUSE OF THE UNCLEANNESS OF THE CHILDREN OF ISRAEL — i. e. for those who entered the Sanctuary in a state of uncleanness without having finally become conscious of this fact (Shevuot 7b), for it is said לכל חטאתם, and the word חטאת implies a sin committed unconsciously.

השכן אתם בתוך טומאתם, “that dwells with them amidst their contamination.” Even though the Jewish people are contaminated the Shechinah is amongst them (Sifra Acharey 4, 5). This is the opinion of Rabbi Yehudah in the Talmud Sukkah where he states his view that one may cover the Sukkah with material which is subject to becoming contaminated, although his view is not shared by the other scholars. He based his opinion on the text in our verse.
We also have an opinion in Sanhedrin 37 according to which the words וירח את ריח בגדיו, “he inhaled the fragrance of his clothing” (Genesis 27,23) are understood as וירח את ריח בוגדיו, “he inhaled the fragrance of those who betray Him,” i.e. even though the person concerned is contaminated, seeing that they are Jews G’d does not totally reject them. Another allegorical approach along these lines is found in Shemot Rabbah 33,2 where the word עלית למרום שבית שבי (Psalms 68,19) are understood to mean that even if there were unfit Jews amongst the people this did not stop the Shechinah from being amongst them. The Midrash understands the words as a rebuttal to the Gentiles who believe that because Jews have served idols at one time they are forever cut off from G’d’s grace.
Another comment by the Midrash (Bereshit Rabbah 18,8) on the words of Maleachi 2,16: “for I detest divorce- said the Lord G’d of Israel,” points to the fact that the prophet Malachi when mentioning G’d always uses the expression אלוקי צבאות, and only in this instance does he refer to G’d as אלוקי ישראל, “the G’d of Israel.” The author of the Midrash sees a clear message in this that the prophet wanted to reassure the people that G’d’s presence does not abandon the Jewish people even when they are sinful.

In [a state of] impurity. Explanation: For being in impurity and inadvertently entering the Sanctuary or [eating] its sanctified items. However, [the verse is] not [speaking about] the impurity of idolatry or promiscuity or murder which are also called impurity. This is because it is written, “He will atone for the Sanctuary.” This indicates that it is speaking about the impurity of the Sanctuary and its sanctified things. See the Gemara, first chapter of Shavuos (7b), where this is explained well.