It can happen with any bullet, but you're probably thinking of frangible rounds, which are designed to do that so as not to overpenetrate and risk harming bystanders.

Ammo which is designed to disintergrate on imact with a surface that is harder then the bullet itself, it is used in most "green" ranges or a lot of out door ranges concerned with lead

Used for training purposes, it is generally loaded with a frangible bullet. This is a bullet made of sintered metal (metal powder squeezed in a mold). On impact with a hard surface, it breaks apart into powder, reducing the hazard of ricochets.

Yes

It does not.