Insulating food on Erev Yom Kippur:
Some rule it is forbidden to insulate food on Erev Yom Kippur for one to eat after Yom Kippur. Others however rule it is permitted to be done. The latter opinion is the main Halachic opinion, nevertheless the custom is to be stringent like the former opinion.
May one leave food cooking over a fire on Erev Yom Kippur for the sake of eating on Motzei Yom Kippur?
Based on the above custom one may not do so.
May one leave food cooking over a fire on Erev Yom Kippur for the sake of children or an ill person?
Yes. In such a case it is permitted to leave food over the fire, or insulate food before Yom Kippur, whether they plan to eat the food on Yom Kippur or desire to have the food ready to be eaten immediately after Yom Kippur.
 First opinion in Admur ibid; Rama 609/1
 The reason: The reason for this is because insulation was only allowed to be done in honor of Shabbos, however for the next day it is forbidden to insulate as it is considered like Yom Kippur is preparing for a weekday. [ibid]
 Second opinion in Admur ibid; Michaber 609/1; Tur
 The reason: As only an action done on Yom Kippur is forbidden when done for the weekday, however if an action which prepares for a weekday occurs on its own on Yom Kippur, there is no prohibition in setting it up before Yom Kippur. [ibid]
 Piskeiy Teshuvos 609/1
 Alef Hamagen 609/1; Piskeiy Teshuvos 609/1