There is yet another existential connection between Purim and Yom Kippur.
On Purim Klal Yisroel faced physical annihilation. The edict was enacted: “To destroy, to slay and to exterminate all the Jews” (3:13).
On Yom Kippur, Klal Yisroel had been slated for a similar fate. Hashem told Moshe Rabbeinu, “Release Me, and I shall destroy them and erase their name from under the heavens, and I shall make you a mightier, more numerous nation than they” (Devorim 9:14). In response, Moshe fasted for forty days and nights and davened to Hashem. Ultimately, his prayers were effective, and the decree was repealed.
Thus, on both Purim and Yom Kippur there were gezeiros for annihilation looming over the Jewish people. A fundamental difference between these two decrees was that while on Purim the imminent threat was public knowledge, on Yom Kippur the Jews had no idea that Hashem was contemplating their destruction. Hashem made the gezeirah in Shomayim, and Moshe was the only one who was aware of it.