Normally, a cat will be fine if it is hungry for a day, but if it is a kitten under two months old, or a weak or sick cat, it may cause damage to the liver function or even death. Therefore, it is best not to let the cat starve for a day, especially if it cannot cut off water. If the cat has no appetite, you can feed it some canned food to stimulate appetite, and you can also feed it some probiotics to help regulate the intestines.