Teacup Shih Tzus in general are more prone to health problems because they were intentionally bred for a small size above any other concerns. Free teacup dogs may be more likely to suffer from these problems, because otherwise their previous owners would generally be charging money for them.
The American Shih Tzu Club does not recognize teacup Shih Tzus, and teacup breeders are often known for having poor breeding practices. They often do not do necessary health testing for genetic diseases. They also breed poor-quality dogs that do not meet breed standards if the dogs are sufficiently small. Teacup dogs often sell for more money than full-size Shih Tzus despite these health problems.