Participial Phrases (Non Finite)

A. Participle Phrase Modifying Noun or Pronoun ---> Adjective/relative clause reduction-->verbals as adjective

Position :

After the noun being modified :

a. noun as subject

    The man talking to the teacher is very intelligent.

b. noun as object of verb

    Anna knows the girl talking to the teacher.

c. noun as a complement of verb

    The person to see is that man talking to the teacher

    This is a good government, supported by all the people

d. noun as object of preposition

    Anna is interested in the man talking to the teacher

At the beginning of the sentence (modifying the subject)

Supported by most people, the new President felt confident about the future

At the end of the sentence (modifying the subject)

The new President felt confident about future, knowing that he had the support of all the people

B. Participle Phrase Modifying as Part of the Object of a Verb

After verbs of perception (feel, hear, see, watch, observe, observe, perceive)

I heard him talking to the teacher.

I saw them running across the street.

C. Other Sources

Reduced Relative Clause --> Participle Clause (Non Finite)

what is ellipted is a WH word/relative pronoun and some form of be

The person reading a book did not hear my question ---> who was reading a book 

The police found the picture stolen from the art gallery --> which had been stolen form the art gallery

Reduced Adverbial Clause --> Participle Clause -

what is cut out or ellipted is a  pronoun and some form of be

While he was sitting at the table, Willy wrote a long letter to Anne.

---> While sitting at the table, Willy wrote a long letter to Anne; or

---> Sitting at the table, Willy wrote a long letter to Anne

When he looked outside, he saw the police car ---> Looking outside, he saw the police car.

Because she didn't feel well, she sat down --> Not feeling very well, she sat. down

Because it was barking loudly, the dog scared us --> Barking loudly, the dog scared us.

Because it was barking loudly, we were cared ---> CANNOT BE REDUCED (the subjects of the main clause and the adverbial clause aren't the same)

We can form reduced adverbial clause with having + past participle for an earlier action, usually instead of a past perfect.

 After he had retired, Ben decided to travel --> Having retired, Ben decided to travel.

We use being + Past Participle instead of a passive.

I was really quite flattered at first, because I was asked to work with one of the professors -->

I was really quite flattered at first, being asked to work with one of the professors

We can also form reduced adverbial clauses by using subordinating conjunctions such as before, as if, after, since, when, while with a present participle.

Before you leave, switch off all the lights --> Before leaving, switch off all the lights 

He stood there, as if he was waiting for someone --> He stood here, as if waiting for someone.

Reference

Frank, Marcella. 1972. Modern English : Exercises for Non-Native Speakers, Part II Sentences and Complex Structures. New Jersey : Prentice Hall Inc.

Miller, Jim. 2008. An Introduction to English Syntax. Edinburgh : Edinburg University Press Ltd

Yule, George. 2023. Advanced Oxford Practice Grammar With Answer. Oxford : Oxford University Press.