Between what?
Whether the box is above, below or on the line, all corners go to the vanishing point(s). In one pt., the horizontal lines are parellel and the vertical lines are parellel. Depending on where you put the Vanishing Point, all lines go to the VP from every corner. In 2 pt. perspective, vertical lines are parallel but Horizontal lines are determined by lines going from the corners to the VP's.
In both cases if you don't indicate where the box ends as it goes to the VP it will appeat that that end of the box disappears.