A picky cat may refuse to eat, but they will not necessarily starve. However, not eating for an extended period of time can lead to serious health problems, such as liver and kidney dysfunction, decreased immune function, and muscle wasting. If your cat is being selective with their food and not eating enough, it's important to consult with a veterinarian to determine the underlying cause and to develop a personalized feeding plan to meet their nutritional needs. Your veterinarian may also recommend feeding smaller, more frequent meals, offering a variety of foods and flavors, or using food puzzles to encourage your cat to eat.