I saw other phrases like Tom doing the homework, Jane cleaned her room.
But I'm not sure with this sentence: He doing the homework, Jane cleaned her room.
Is it possible to have pronoun in subject form as the subject in participle phrase?
I saw other phrases like Tom doing the homework, Jane cleaned her room.
But I'm not sure with this sentence: He doing the homework, Jane cleaned her room.
Is it possible to have pronoun in subject form as the subject in participle phrase?
Neither of your sentences is correct English. You could say
While Tom was doing his homework, Jane cleaned her room.
If Tom was mentioned in the previous sentence, so we know who you are talking about, you could say While he was doing his homework... instead.
Tom doing the homework, Jane cleaned her room.
It's acceptable if "He doing the homework" is intended to be an adjunct of implicated reason, i.e. the adjunct gives the reason for the matrix situation (Jane cleaning her room).
Yes, a subjective pronoun is fine, as is an objective one: "He/him doing the homework ...".