Why did the cat's whiskers break? Is it sick?
There are three possible reasons why a cat's whiskers might break: it's a normal physiological phenomenon due to its advanced age, it's a normal phenomenon of growth and development, or it's a sign of illness.
1. When a cat loses its whiskers, consider its age. Many cats' whiskers turn white as they age. At the same time, the cat's whiskers will fall out. Note that this is a normal physiological phenomenon in cats and a signal of their aging metabolism.
2. Don't worry if your kitten's whiskers break; this is a very normal phenomenon in a cat's growth and development. As the cat grows to a certain stage, its teeth and fur will grow back, and its whiskers will fall out and grow back.
3. Besides these two reasons, a cat's whiskers can also fall out, and this is a major cause of whisker loss. There are two basic situations: skin diseases or nutritional/metabolic diseases. Simply put, if a cat's fur is infected with bacteria and fungi, it will cause skin diseases, and the whiskers will fall out. 
The function of cat whiskers:
In short, a cat's whiskers function like antennas. The tips of the whiskers help it detect obstacles in its surroundings. When hunting or escaping from enemies, cats must navigate very narrow spaces and simply don't have the energy or time to check every obstacle coming from the front.
Cats naturally have difficulty focusing their eyes on the edges of their field of vision, making it hard for them to assess their surroundings. That's when they rely on their whiskers. If the tip of their right whisker touches something, it means there's an obstacle on the right, and they'll move to the left, much like how we grope our way forward in the dark.