Let's not get obsessed with the word "modify"!

Suppose, for example, that we have these sentences.
I accidentally dropped a plate on the floor.
This caused the plate to break.
In what sense does the second sentence modify the first? In my opinion, there is nothing about the first sentence that is altered (modified, changed) by the presence of the second sentence. The second sentence simply adds more information to our narrative of what happened. The second sentence does, however, contain the word this, which references the entire first sentence, i.e., This (previously mentioned event) caused the plate to break. The participial construction you are concerned with in this thread is nearly identical in function, but the reference word this is left out. It is merely implicit.
I accidentally dropped a plate on the floor, causing it to break.
Since the participial construction adds more information to the entire sentence which precedes, it may be called a sentential adverbial, in my opinion, but the search for anything more specific that it modifies is doomed to failure! 
Similarly, note that in any compound sentence, the second clause does not modify the first. I am hungry, and John is thirsty. This participial construction is not much different, except that the logical relationship of the added participial is closer to the situation expressed in the first clause. We should keep this in mind.
CJ