Does the dog know that the owner is sad and crying?

The dog knows that the owner is sad and crying. Research shows that dogs can sense their owner's emotions from changes in their owner's voice. So, when you are sad, your dog will stay with you or come up to smell what is wrong with you. Dogs are very understanding of human nature. Whether their owners are sad or losing their temper, dogs are aware of it.
So when a dog does something wrong, he will hide away with his tail between his legs. This is also the same reason.