.....Alex leaving the cafe and refusing to

[JEic]

In this original sentence, can I use a subject + a gerund? If it is okay,

- It refers to Alex leaving the cafe and refusing to continue with the conversation.

The sentence sounds right but I am unsure; can I use "Alex + present participle" in this manner? If it is correct, why?

Is there such a thing called "object phrase"?

 

[emsr2d2]

In this original following sentence, can I use a subject + a gerund? If it is okay, Is it okay?

"It refers to Alex leaving the cafe and refusing to continue with the conversation."

The sentence sounds right but I am unsure; can I use "Alex + present participle" in this manner? If it is correct, why?

Is there such a thing called as an "object phrase"?

There might be a grammatical term for it, but it's certainly correct. I would describe it as a shorter version of "It refers to Alex, who is leaving the cafe and refusing to continue ..." or of "It refers to Alex's actions of leaving the cafe and refusing to continue ...".
A grammar expert might be able to answer the rather odd "If it is correct, why?" and the question about an "object phrase". I'm a "use of English" teacher, so I don't get too involved in the grammatical intricacies of the language.