The Minchas Chinuch and R' Akiva Eiger (Shu"T #16) raise the question of whether women are obligated in the mitzvah of eating on erev Yom Kippur. On the one hand, since the mitzvah can only be performed on erev Y"K, it would seem to be a classical mitzvas aseh she'hazman gerama. On the other hand, the gemara tells us that one who eats on erev Y"K gets credit as if he/she fasted two days. Since women are obligated in the fast of Y"K, perhaps they should also be obligated in this eating which serves as a kiyum of the ta'anis.
The relationship between the mitzvah to eat and fasting is further reflected in why we eat and what we eat. Rashi (Yoma 81b d"h kol ha'ochel) writes that eating is necessary simply to prepare for the fast. According to Rashi a simple meal of bread and water might suffice so long as it fills one before the fast. However, other sources indicate that eating is not just preparatory to the fast, but is an end in its own right and should be fulfilled with the finest foods. The Tur quotes a story of a poor man who spent his fortune on fish for the erev Yom Kippur meal; Rabeinu Yonah (S.T. 4:8) suggests that the eating on erev Y"K is a substitute for the simchas Yom Tov celebratory meal we lack on Yom Kippur itself. Whether one who is ill and cannot fast must fulfill the mitzvah of eating may hinge on which of these approaches is correct.
The gemara illustrates the principle of "mutav she'yeheyu shogigin v'al yehu meizidin" by pointing to our tolerance of women eating and drinking right up until twilight on erev Yom Kippur, ignoring the mitzvah to add a few minutes of the weekday onto the observance of the fast. The Rabbis thought it better to not inform women that they should stop eating earlier because their warning would likely be ignored; what had been done in ignorance of the law would continue to be done in violation of any warning, with no gain in observance. At first glance one might read this gemara as patronizing toward women in not trusting their commitment to the din of tosefes. However, the Halichos Beisa in his introduction cites an explanation of the Torah Temima which puts things in a different light. There are so few mitzvos aseh she'hazman gerama which women are actually obligated in that women relish the chance to do these mitzvos. An example of this type of mitzvah is eating on erev Yom Kippur (we see which side of R' Akiva Eiger's safeik the T"T was on)! In their enthusiams to perform this mitzvah to its fullest, women continued to eat right up until the last moment before Yom Kippur. Rather than throw cold water on their love for the mitzvah, Chazal felt it better to remain quiet and allow the practice to continue.