How to make path vertex follow object's position

The Window/Create Nulls from Paths.jsx.Points Follow Nulls script can add a pair of nulls to the path. You could then tie the position of the lower right null to the position rectangle with parenting. Move the rectangle, and the point will follow. 

You could also use the same script with the Trace option to create a null that would follow the shape of the rectangle (if it was a bezier path) or the Nulls follow Points option to tie the null on one end of the path to any vertex or the path of the rectangle.