A sentence fragment is an incomplete sentence. Some fragments are incomplete because they lack either a subject or a verb, or both.
This particular sentence lacks a verb. "the marionettes" is the subject of the independent clause. "Operated by wires above the stage" is a participial phrase modifying the subject, i.e. providing some description about the subject; "whose features seemed lifelike" is a dependent clause describing the subject.
As we see, there is <u>no verb to clarify the subject</u>. What does the writer want to say about "the marionettes"? What did they do? or What were they? We have a written fragment, a major writing error.
This is a fragment because the sentence cannot stand on its own. It does not contain a compete thought. The reason it does not contain a compete idea is that it has no verb in it.
He offers Nick part in a business that he does on the side line in which he would a great deal of money Nick now realized that Gatsby was not used to people doing favors for him without requesting something in return he also realized that Gatsby was lonely and did not have true friends