How to use supplementary -ing clauses at the end of sentences

Question

I'm wondering how to use those "(noun-y) -ing clauses" when they are at the end of the sentence. Most grammar references I've found on the internet only talk about their use as adverbials at the beginning of a sentence. For example:

1) Wanting more money, he accepted the offer.

But I've seen many times people put them at the end of sentences:

2) He issued an attack on her at the company, describing her as an amateurish programmer.

3) She ran all the way to the playground, her friends following.

In these last two examples above, the -ing clauses don't look like adverbials to me. They can be paraphrased as separate sentences. I feel like, because they are related, instead of writing two separate sentences, the writer combines them together.

Grammatically, what are those types of -ing clauses called? And when is it appropriate to use them?

Answer 1

The -ing phrases are participle phrases.

They are allowed at the end of sentences, but you want to be careful that you don't accidentally make a misplaced modifier:

*"Steve stood and watched a man, running his hands through is hair." This sentence is not good because it is hard to tell if Steve running his hands through his hair, or if the man Steve watches is running his hand through his hair.

You can use participle phrases as long as it is very clear which noun they modify.

Answer 2

/describing her as an amateurish programmer/ is dangling. It comes from "And he describes her as ........" The first subject /he/ can be NOT related to the object of speaking /her/.