I think a participle clause and main clause having different subjects is exception to the rule of participles. I found the following sentences in a grammar book and in some internet resources which I suppose to have different subjects:
- The weather being nice, we decided to go for a picnic.
- It being a cloudy night, I couldn't see the moon.
- Saroj being late, I couldn't catch the bus.
All of them contain "being". It would seem that we can use different subjects in participle clause and in main clause with the help of being. Are they correct sentences to use? Are there any other conditions when we can use different subjects in a participle clause and in main clause, or in subbordinate clause and main clause? I've read this source too: https://english.lingolia.com/en/grammar/sentences/participle-clauses