A cancer patient who cant use his mouth has his food going straight into the lower stomach using what is called a peg. It is a milk based food which is considered kosher but not for pesach according to the kosher guide. My question is if one can use this on a taanis, if it is considered eating. Also if yom kippur maybe different since there, taanis is not mentioned but inui which may not be the same but more strict. Also if the person has absolutely no appetite so he would not feel the fast anyway would it make a difference.
The Falk-Shlesinger Institute for Medical Research according to Torah associated with Shaarei Tzedek hospital has a long article on artificial feeding on Yom Kippur.
It asks three questions, one of which is
יש להסתפק מה הדין כשאוכל ביום הכפורים ישר למעיו דרך החלחולת או דרך אינפוזיה האם חייב משום איסור אכילה ביום הכפורים אם לאו?
What is the ruling on eating on the Day of Atonement straight to his bowels through the rectum or through infusion? Is it obligatory for him to refrain from eating on Yom Kippur or not?
The summary conclusion is
כפי המבואר בדברי המהרש"ם והאחיעזר דאף לדעת החתם סופר דהנאת מעיים בעינן לחיוב ביום הכפורים, אבל כל זה בנכנס דרך גרונו אבל בנכנס דרך מעיו ע"י חוקן או ע"י דרך אחרת אין חיוב ביום הכפורים.
As explained in the words of the Maharasham and Ahiayzer that even according to the opinion of the Chatam Sofer, the internal satisfaction does create liability on the Day of Atonement, but only if this comes through his throat. But when the food enters through his intestines by enema or by another way, there is no liability on the Day of Atonement.
So we see that even on Yom Kippur, he would not be liable for such internal feeding (and even less on a normal fast day). The text speaks about "liability" but you ask about whether internal feeding is considered eating at all. This point could be further discussed.
May Hashem grant all patients a complete healing.