Grammar Help, Please.

[abracanabra]

I can't find the correct terminology for this sentence construction, and it has been driving me mad! What is it called when you use a comma to join an independent and a dependent clause without a conjunction--correct only if they describe actions that switch tense from past to present.

For example, "She ran for the door, grabbing her purse as she went."

Would the second clause be a coordinate verb phrase?

I know this is rather technical, but it's bugging me a lot to not be able to use the correct terminology when noting incorrect use.