Thanks saruba! Good input!
SC drives me nuts so bear with me

I just try to understand everything there is on this naughty subject (or at least as much as possible) so that I can beat every single SC question...
OK, here the sentence again:
Stella Adler was one of the most influential artists in the American theater, training several artists [...]
And here some thoughts on participle phrases--> the
only reason we use participle clauses is to reduce a sentence:
For example: if two sentences have the same subject, we can reduce one part to a participle clause:
No participle construction: She watched TV. She forgot everything.
With participle construction: Watching TV, she forgot everything around her.
Now, bringing it all together:
Stella Adler was one of the most influential artists in the American theater. She trained several artists [...].
When I reduce the second sentences by using a participle construction, I get
Stella Adler was one of the most influential artists in the American theater, training several artists [...]BTW: of course, participle constructions can be used for a number of things not just reducing one sentence that shares the same subject with another sentence (such as *not like

* relative clauses)