Past a certain age, cats tend to develop that specific physique as they lose muscle tone — usually around 17 or 18 years old. By that point they probably also have arthritis making grooming more difficult/painful, which can contribute to the "mangy" look of their fur. Of course, age itself also affects the fur in various ways including thinning and changes in luster/texture. It's also very common for senior cats to have some sort of kidney disease, which can lead to dehydration that further affects the fur.