Like something you might buy from a shop, if they are damaged goods they are not fit for purpose. For example, you might be thinking of offering this man a job in a bank, but if he has a criminal record he is damaged goods, you can't.

you don't need to include the "a" you just say he/she is damaged goods meaning they have been emotionally or physically damaged in some way due to traumatic events that may have happened in their life. so they may be depressed, emotionally unavailable or unstable.