This is a question thrown up by the Google search engine. Cats’ whiskers do not normally break. They fall out and a replacement is grown but they don’t break unless, in an otherwise healthy cat, there are perhaps dietary problems causing the whiskers to be fragile. Apparently, vitamin A is a requirement for the synthesis of keratin and whiskers, as you may know, are made of keratin. Perhaps they are less robust if a cat’s diet is deficient in vitamin A. Although a cat caregiver should not give their cat an excess of vitamin a because it becomes toxic if you do. Although, fish liver oil, liver and egg yolks are a good source of vitamin A. However, standard cat food will contain all the vitamin A that a cat requires. That said, the whiskers of a healthy adult cat may occasionally break in rough play but I would suggest that this is rare.
Hairless cats
I think the question in the title is really about the hairless cats. Hairless cats do have thinner, crinkly and shorter whiskers than normal if they have any at all. Often, they are missing (see video below). They are more fragile and therefore they break. You will find hairless cat owners saying that their cat’s whiskers break fairly often.
And the reason why the whiskers of hairless cats break is because the recessive gene which causes hairlessness, affects the creation of the whiskers to the point where they become weakened.
Hairless cats have occurred spontaneously throughout the world including in France, Canada and England. This abnormal deficiency a hair is called hypertrichosis and it is due to the presence of a recessive gene indicated by the letters h, hr, and hd respectively in reference to the country of origin above. The Canadian hairless cat is the well-known Sphynx cat that is quite popular today.
Below are some more pages on cats’ whiskers. Please comment if you can add useful information.