The "black line" is when the actual break begins. The shaded area between that and the last note is a time where there's no HP Drain, but the break stuff like the black bars aren't there.
Best way to show this is to put your mouse cursor at the "black line" so you get a resize cursor, and then drag the beginning of the break a long ways to the right. Then, playtest the map. You should see what I mean. It's like what happens in EBA and Ouendan, if you played those games.
So yes, you should pay attention to this. It acts like this so that when you want the break to start on a specific beat to, say, match with the Storyboard, you can do so without causing the HP to drain while there are no hit objects to hit. But, if you have the break start at a random point (like shown in your example) and not a specific beat, it's ugly and should be fixed.