There is a lot of controversy and misguided information online about teacup dogs.
You see there are breeds who have a developed gene that stunts the size of the dog, and there are runts. Also there different variations of the smaller structure genealogy.
Take the poodle for example, they have teacup poodles, that are just the smaller variation of the toy poodle, perfectly healthy, but cannot be bred.
Why cant they be bred? Well they do not have the many generations behind them supporting that gene, such as some Yorkie do.
Also you must be careful that you do not buy a runt, lots of breeders well sell a runt as a teacup. always ask the parents size. and NEVER BREED anything smaller then four pounds! You don not know if the lines support the size, but by word of the breeder, its not a risk worth taking.
A true teacup has generations of the smaller structured genes along the blood line.

They are just as healthy as the big ones. but of course sense they are smaller they can easy get hurt if stepped on, or played ruffly with.