There is a big difference between 'He died happily' and 'He died happy'. "He died happily" would describe the actual WAY that he died - as though he was delighted to be dying and did so smiling and laughing. This seems unlikely! Compare this with 'I'll happily help you", meaning that I will be happy to help you, or even that the act of helping you will give me pleasure. As you can see, this is different from the situation above. While the act of helping a friend can give you pleasure, it seems impossible that the act of dying could give the person pleasure. Quite the opposite, one would imagine. By contrast, "He died happy" - and you can even imagine a comma before the word 'happy' - means that he died at a stage in his life when he was happy. It means that he had achieved what he wanted in life, so he was happy at that point - hence the use of the adjective. Likewise, 'He died broke' is correct, because 'broke' (meaning 'penniless') has nothing to do with the manner in which the unfortunate man took his dying breath - it describes his financial state at the time of his death. Hence the adjective. It's the same with your other two examples: "He came back drunk" doesn't describe his manner of returning (as in "He came back slowly") - it tells us the state that he was in when he came back. "I was standing there stunned" doesn't describe your physical posture (the 'way' you were standing) - it tells us how you felt at that moment. This is one case where the comma would be appropriate. If you write it as "I was standing there, stunned", is that clearer why we use an adjective?

"He died happily" actually does make more sense than "He died happy". However, the english term "He died happy" doesn't literally mean that this man had died/expired/deceased and he was happy whilst he was dying. "He died happy" means that this man was happy in life, and then he died. So happy is actually a describing word for him. An example of this might be: A blue man has just died. "He died blue" A bald man has just died. "He died bald" A happy man has just died. "He died happy" All of your sentences make sense too :) I hope this helped :)

Yes, those are all "flat adverbs". Even though they look like adjectives, the word-order tells us that they work as adverbs. https://en.wikipedia.org/wiki/Flat_adverb