Helpless means unable to protect oneself or act effectively.
The sentence "He quarreled with his boss helpless of the consequences" means he quarreled without being able to avoid or control the consequences.
Although it’s a bit unusual phrasing (more common would be "regardless of the consequences" or "unaware of the consequences"), helpless fits better than headless (which means without a head) or both.
“Headless” literally means “without a head,” and is mostly used literally or metaphorically to describe something done without leadership or direction (like a “headless chicken”).
In the sentence:
He quarreled with his boss ___ of the consequences.
Using “headless” here is not standard or correct English because it doesn’t make sense to say someone acted “headless of the consequences.”
“Helpless” means lacking power or ability to do something, so if the sentence is trying to express that he was powerless about the consequences, “helpless” fits better.
However, the sentence sounds a bit awkward in both cases; a more natural phrase would be “regardless of the consequences” or “without regard to the consequences.”
