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.
Wait, you guys are getting President’s Day off work??