Cats might starve themselves. On several occasions over the years, a cat will starve itself before eating a particular type of food it does not like. Cats, unlike dogs, have strong preferences when it comes to their diet. They would simply not eat the food if they do not like the smell and the taste. There are many other reasons why the cats can starve themselves. Whatever be the case you cannot let a cat starve for more than 24 hours because they can develop liver problems.