When baby plays with toys, or household items like cups and plates, the occasional break is inevitable. You don't need to make a big deal out of breaks, so that baby becomes shy about handling anything. But, you do want to be matter-of-fact that the item is broken and is not coming back, so that baby realizes that it is not something they want to happen again and they'll be more careful in future.
One of the main goals of baby sign language is to equip your little one to convey concepts that can be frustrating. We like the sign for broken because it equips your baby to let you know that something has gone wrong. Our little ones love to use it when they are trying to let us know about a toy that does not work.