I had seen on this Halachipedia page in the name of R' Shlomo Zalman Auerbach that one may drink a minimal amount of water, as needed, in order to swallow pills. However, R' Belsky, as quoted in this article, forbids such a practice. However, all opinions, as also brought down in the latter article, agree that one should avoid it on Tisha B'Av, if possible, and that its 100% forbidden on Yom Kippur. (This is assuming you don't have doctor's orders. Even R' Belsky agrees you should take the pills with water on Yom Kippur if a doctor tells you to do so - same article.)
What about one who needs to take a pill, but such a pill requires him or her to take it on a full stomach? Is one allowed to have something to eat in order to take the pill? Does it make a difference if he's a choleh sheyeish bo sakanah or not? In any of the above scenarios, including where you're just drinking water, is one considered to have "broken his/her fast" after having more than a reviis of liquid or a kekoseves of food, such that there is no longer a prohibition to eat? (I don't have a source for that last claim, but I'm pretty sure I learned somewhere that on any fast day besides Yom Kippur one can only be oveir eating/drinking once. Please correct me if I'm wrong.)