בַּיּ֤וֹם הַשְּׁמִינִי֙ שִׁלַּ֣ח אֶת־הָעָ֔ם וַֽיְבָרֲכ֖וּ אֶת־הַמֶּ֑לֶךְ וַיֵּלְכ֣וּ לְאָהֳלֵיהֶ֗ם שְׂמֵחִים֙ וְט֣וֹבֵי לֵ֔ב עַ֣ל כָּל־הַטּוֹבָ֗ה אֲשֶׁ֨ר עָשָׂ֤ה יְהוָה֙ לְדָוִ֣ד עַבְדּ֔וֹ וּלְיִשְׂרָאֵ֖ל עַמּֽוֹ׃
Le huitième jour, il congédia le peuple, qui bénit le roi; et ils rentrèrent dans leurs foyers, heureux et le cœur réjoui de toutes les grâces dont Dieu avait comblé David, son serviteur, et Israël, son peuple.
Akeidat Yitzchak
The reason that sins committed between different human beings are not subject to atonement of Yom Kippur is, that any sin in which man's body is the major party, can only be atoned for by that same body making the appropriate restitution. When reconciling oneself with one's fellow man, it is the senior person, the scholar, who must make the first move, just as Abraham had done with his nephew Lot. (Genesis chapter 13)