There is a well-known saying quoted in the name of the great Rabbi Levi Yitzchak of Berdichev that Yom Ha’Kippurim (Yom Kippur) is like Purim. This means to say that the salvation of the Jewish nation during the days of Purim came about through Yom Kippur.
This can be explained based on the commentary of Hagaon Rabbeinu Yehonatan Eibeschitz on Megillat Esther.
The Megillah states: “When King Achashverosh sat on his royal throne, he made a feast for all of his officers and servants for many days, amounting to one hundred and eighty days. When these days were completed, the king made a feast for all the residents of the capital, Shushan, for seven days etc.”
We all know that the Jews participated in the one-hundred-eighty-day long feast but their enjoyment at the feast of the wicked King Achashverosh constituted a grave sin.
The commentators write that Achashverosh counted the years of his reign beginning with the month of Nissan in accordance with the custom of Jewish kings (non-Jewish kings counted from the month of Tishrei, see Rosh Hashanah 3a). Thus, Acheshverosh’s feast began from the day of Rosh Chodesh Nissan. It is for this reason that the verse uses the words “many days” which alludes to the fact that the actual days were long, for all one hundred and eighty days of the feast were held during the long summer days.
When we calculate one hundred and eighty days beginning from Rosh Chodesh Nissan, the conclusion of this feast was on the Third of Tishrei (for this amounts to six months, three comprised of thirty days each and three comprised of twenty-nine days each). On the Third of Tishrei, Achashverosh began the seven day feast for the residents of Shushan, including the Jews of Shushan who did not heed the warning of Mordechai and partook of this feast. Thus, there was source of defense in Heaven to protect the Jewish nation from the plot of the evil Haman since they participated in Achashverosh’s party.
Nevertheless, on the seventh day of the feast which coincided with the Tenth of Tishrei, Yom Kippur, all of the Jews went to the synagogue on the holiest day of the Jewish calendar; thus, on this day, not one Jew participated in the feast of Achashverosh.
At this point, the Heavenly angels found a way to speak in defense of the holy Jewish nation and immediately, Hashem was overcome with mercy and on that day, Achashverosh decreed that Vashti be killed which set the stage for Esther to be chosen as queen and ultimately led to the downfall of the wicked Haman.
Tus, we see that the merit of observing Yom Kippur saved the Jewish nation from certain annihilation on the day of Purim.
May Hashem grant us the merit to see much salvation and consolation as did our forefathers at that time during this period. May Hashem likewise once again redeem us eternally and send our righteous Mashiach and build the Third Bet Hamikdash, speedily and in our days, Amen. Happy Purim!