A student of mine asked me this question based on an application he was filling out. I am assuming there is a historical or halachik answer to this question.
"When was the one time the Jewish people did not fast on Yom Kippur?"
The first Holy Temple was inaugurated by King Solomon on the 8th of Tishrei, and was celebrated for the next 14 days. In that year they did not fast on Yom Kippur, which fell right in middle of the festivities. The sages worried that they had erred in the matter, but a heavenly voice proclaimed that all those who had participated in the inauguration of the Temple would merit the World to Come.
In 1848, Rav Yisra'el Salanteer ordered Jews of his town to eat on Yom Kippur because of the dangers of the cholera epidemic.
It was to him a matter of "when we have to act for the sake of God; then the law must be dispensed with. "In a place where there are no men, strive to be a man." Then he ordered announcements to be posted in all synagogues urging a dispensation of the fast. The people, however, were hesitant about complying, as indeed he felt they would be. At the very solemn moment after morning services (Shaharith) before taking out the Torah from the ark, the beadle ascended the platform, demanded that there be silence and made the following announcement: "By the Knowledge of the Omnipresent One, and by the authority of the Torah we grant permission — because of the epidemic — to eat and drink today." No one, however, stirred, no one dared to leave his place, holy terror had stricken them all. Then, to the utter amazement of all, Rabbi Israel, the meek unobtrusive Rabbi Israel, followed the beadle on the Reader's platform and in a solemn, muffled voice exhorted the congregants to abide by the decision just proclaimed.