Illustrator Width Tool: Make Closed Shapes look like Open Paths

One of the basic properties for the Width tool is that you can drag a Width point over another one. When the widths are different and the points overlap, the Width Profile forms a sharp transition (such that you can make an arrow, for instance).

Utilizing the same trick, you can make a closed illustrator path look like an open path by having a segment of the line have zero widths! Just overlap width points over other width points at the right transitions!