Comma or no comma for Adjective phrase

Solution 1:

It may be grammatical without the comma, but (without further rephrasing) the meaning of the sentence would be ambiguous and could lead to a nonsensical interpretation.

Without the comma, either of these are possibilities:

Jack stood at the door [and was] numb with pain.

Jack was numb with pain.

Jack stood at the door [that was] numb with pain.

The door was numb with pain.

With the comma, you can invert the sentence if you want to understand it in a different visual way:

Numb with pain, Jack stood at the door.

So, if you don't want there to be any possible misunderstanding (I grant it's unlikely anybody would interpret it incorrectly), and if you don't want to rephrase the sentence, include the comma in this sentence.

Note that in the specific sentence considered so far, common sense would typically reason that it can't be the door that is feeling numb.

However, consider this:

Jack stood next to Mary, numb with pain.

Here, it seems clear that it's Jack who's numb with pain, especially since this sentence can still be inverted as before:

Numb with pain, Jack stood next to Mary.

But it's not nearly as clear if we remove the comma:

？ Jack stood next to Mary numb with pain.

Since common sense doesn't rule out Mary being the person feeling pain (as it would with the door), this is a truly ambiguous sentence.

As before, inserting missing words would make the meaning clear:

Jack stood next to Mary [and was] numb with pain. (Jack is numb with pain.)
Jack stood next to Mary [who was] numb with pain. (Mary is numb with pain.)

But there is nothing that clearly shows which of those missing words should be assumed.

Therefore, common sense can't bail us out from this situation. With this sentence, it's even more essential to either use a comma or rephrase the sentence to add those missing words that make the meaning clear.