Chinchilla inbreeding
Most pet chinchillas in the United States are probably descended from 11 chinchillas that were brought into the country from Chile in 1923. They were most likely almost hunted to extinction for fur in the 1800s and 1900s. Today, there are probably only around 10,000 individuals left in the wild. With only 11 individuals to work with, pet chinchillas were most likely the result of severe inbreeding. A lot of pet chinchillas today suffer from malocclusion, which is considered a polygenic trait.
Of course captive chinchilla breeding is not natural and usually involves selectivity, non-random mating is not really possible to observe. Malocclusion is a misalignment of the teeth and because chinchillas are rodents, this is a life-threatening medical condition for them. With inbreeding, or facilitative assortative mating, breeders can breed chinchillas with the cute characteristics everyone loves; thick fur in a variety of colors, a cute squirrely tail, and a stocky body. Captive breeding with this method could also give fur collectors what they want without assisting in extinction of the wild chinchilla.
Wild chinchillas are generally a yellowish gray color to help them blend in with their native habitat in the mountains. Through domestication and selective breeding, chinchillas now come in colors like white, black, blue-gray, violet, and pearl. Some colors are recessive, some are dominant, and some are expressed by dosage and incomplete dominance. Some of these colors most likely arose and were kept in circulation by some degree of inbreeding.
Assortative mating resulting from inbreeding in the wild could be beneficial for the remaining population of chinchillas to select for the traits that were most beneficial for survival in their changing environment (maybe?).
Disassortative mating stemming from inbreeding could also be beneficial for the remaining chinchilla population for keeping unhealthy phenotypes in check, such as a different fur color that does not blend in or malocclusion (if it occurs in wild chinchillas (possibly?).
Sources
Chinchilla Colors - Pet Ponder color genetics
Chinchillas.com Chinchilla Malocclusion
Fun Facts About Chinchillas | Live Science