He being sad, I was sympathetic. (Not sure what the rule is here, but "He" is correct.) I was sympathetic, he being sad. (Not sure what the rule is here, but "he" is correct.) I was sympathetic to him being sad. ("Him" the object, the guy who is sad.) I was sympathetic to his being sad. ("His being sad" is the object, but "his" grammatical role is as possessor of sadness.) I was sympathetic to whoever was sad. ("Whoever" is the subject of "was sad.")
no subject
He being sad, I was sympathetic. (Not sure what the rule is here, but "He" is correct.)
I was sympathetic, he being sad. (Not sure what the rule is here, but "he" is correct.)
I was sympathetic to him being sad. ("Him" the object, the guy who is sad.)
I was sympathetic to his being sad. ("His being sad" is the object, but "his" grammatical role is as possessor of sadness.)
I was sympathetic to whoever was sad. ("Whoever" is the subject of "was sad.")