Adverbial clauses can be reduced by omitting the subject and the verb to be:
While I was watching TV , I fell asleep.
While watching TV , I fell asleep.
Why this happen?
He was sent to hospital after he was attacked by a man.
He was sent to hospital after being attacked by a man.
Why does the reduced version in bold have the word being inserted?
Thanks in advance
As far as the subjet is the same in both sentences I guess you can do it, but what happens when the subject is different?
While he was watching tv, I came in
Simply you can't, because if you did it would sound quite weird. No one would know who was doing such a thing.
Regarding the second example both the subordinate and the principal sentences have the same subject.
I was taken to hospital after he bit me , you can’t say: I was taken to hospital after biting me ?????
Neither a teacher nor a native English speaker
Try looking at the difference between "while" and "after" as well who is the subject.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.