The elimination of "with"

[simile]

In this sentence:
A man was standing at the door, his hands in his pockets.
There's an elimination of the word "with."
The original sentence should be:
A man was standing at the door, with his hands in his pocket.
How to explain the part of eliminating "with"?
"his hands in his pockets" is only an NP, not a typical "reduced clause" like we see in sentence like: "Picking up the phone, he dialed 911."
Is this elimination of "with" commonly applied to the sentence like firstly mentioned?
Can students freely use this elimination technique when they write a composition?

[mykwyner]

Sorry, I don't think either of your sentences is accurate English.

A man with his hands in his pockets was standing at the door.

A man was standing at the door; his hands were in his pockets.

[JCrawf]

A second opinion.
I think both sentences are correct, but I'd omit the comma before "with" in the second.
The first is a common construction in written English, but not one that's used in conversational English.

[Humble]

The 1st sentence looks 100% fine to me - a description from a book.

[simile]

Sorry, I don't think either of your sentences is accurate English.

A man with his hands in his pockets was standing at the door.

A man was standing at the door; his hands were in his pockets.

The sentences I put here are all taken from an English textbook.
So from your point of view, maybe I should report to the publisher about their mistakes.

Is this really a wrong sentence?
A man was standing at the door, with his hands in his pocket.

Do you mean even the usage of "with" is also wrong?

[Mariner]

Allow me to offer another opinion

A man was standing at the door, his hands [being] in his pockets

So, we have a non-finite subordinate clause, regardless of the presence of "with". It's the same structure as the other sentence you mentioned: Picking up the phone, he dialed 911.