Participle Clauses представляют собой конструкцию, в которой главное предложение связано с побочным предложением с помощью причастий. Позволяют нам добавить информацию, в экономном виде , есть present participles (going, reading, seeing, walking, etc.), past participles (gone, read, seen, walked, etc.) or perfect participles (having gone, having read, having seen, having walked, etc.).
Примеры: Waiting for Ellie, I made some tea. (While I was waiting for Ellie, I made some tea.)
"Having killed" indicates that the action of killing happened before another action in the clause, while "killing" (present participle) suggests an ongoing or continuous action or a reason for something.
Past participle describes something that has been acted upon, like in "The car accident killed three people" (the people were the subject of the killing). In a participle clause, it would be something like, "The house, killed by the fire, was a total loss," meaning the fire caused the house to be destroyed.