Have a broken heart: This means to be deeply saddened by a loss, usually the loss of a romantic relationship.
Have a broken leg: This is a common expression of good luck, particularly used in the theatre industry. It's an ironic wish as a broken leg would be a major setback for an actor.
Have a broken spirit: This means to be discouraged, defeated, or lacking in hope.
Have a broken record: This means to repeat the same thing over and over, often in a way that is annoying or tedious.
Have a broken home: This means to have a family that is dysfunctional or unstable, often due to separation or divorce.
Have a broken promise: This means that someone has failed to fulfill a promise they made.
The meaning of the idiom depends on the specific word that follows "have a broken." To understand the meaning, you need to consider the context and the word that completes the phrase.