When the subject in the sense of participle structure is the same as the subject of the sentence, is it right to omit the subject and predicate verb in the clause? Please give an example.

I basically understand your question. Let's try to answer. The so-called participle structure includes sentences composed of present participle (v.+ ing) and past participle (v.+ ed). Look at the example of the present participle first: 1. Looking out of the window, I can see the crowded street. Looking out of the window, I saw the street was crowded. Living by the sea, we enjoy a healthy climate. Living by the sea, we enjoy a pleasant climate. The two men smiled at each other and shook hands. They smiled and shook hands with each other. So what is salvation? Take the first sentence as an example, looking out of the window = when I am looking out of the window (omitting the subject I and some predicates are was) and then looking at the past participle. Given more time, she will certainly do better. If she had more time, she would do better. Surrounded by a group of little boys and girls, the old teacher walked into the classroom. Surrounded by a large group of children, the old teacher walked into the classroom. 3. Mistakes and setbacks have taught us to be wiser and handle things better. Mistakes and setbacks have taught us to be smarter and we can do things better. Take the first sentence as an example: given more time = if she is given more time (omit the subject she, part of the predicate have been), and then add another explanation: regarding the present participle, the actions indicated by the three present participles I quoted occur at the same time as the predicate verbs of the main sentence. This also happened later, for example, he continued to speak 10 minutes where he left off. He picked up the topic again and talked for another ten minutes. If it happens before the predicate verb, we should use the perfect tense of the present participle, for example, after sending her son away, the old woman lives alone again. After seeing off his son, the old man lived alone again. Are you satisfied with the above answers?