The question is asked whether a sick person who is permitted to eat on Yom Kippur this year, which falls out on Shabbat, must make Kiddush before he eats. The question is based on the Halacha that one may not eat on Shabbat before making Kiddush. In this case, does the fact that he is permitted to eat reinstate the normal laws of Shabbat? If so, he would have to make the regular Kiddush, with the Beracha of "Mikadesh HaShabbat." Even if he broke his fast during the day, he would make this Beracha, because the Halacha states that if someone did not make Kiddush at night, he must say the Beracha during the day.
Hacham Ovadia, in Hazon Ovadia (Yamim Noraim p. 307), bases himself on the Magen Abraham (Siman 618) and rules that the sick person should not make Kiddush on Yom Kippur. Since it is a fast day for the Jewish People, the Rabbis never established the Misva of Kiddush. Although Rabbi Akiva Eger and Hitorerut Teshuva disagree and rule that Kiddush is recited, the majority of Poskim concur that there is no Kiddush. These Poskim include Rav Svi Pesach Frank (Har Svi Siman 155), the Magen Abraham (as mentioned), Hacham Ovadia Hadaya (Yaskil Avdi Vol. 8 20:34.) This is also the opinion of the Aruch Hashulhan (end of Siman 618). Rav Moshe Feinstein discusses this in his Iggerot Moshe (Hoshen Mishpat, Siman 39)
If one has a valid reason to eat on Yom Kippur that falls on Shabbat, he does so without reciting Kiddush.