When the modules run out, the Timeline fills in the space with more Timeline posts.
As you continue to scroll down the page, you see two equal columns side-by-side all the way back in time to your birth, theoretically.
From a design perspective, the current Facebook Timeline is a train wreck.
The new experimental design makes a lot more sense. It gives more emphasis to the left column by making it wider -- it spans about 60% the width of the page, leaving about 40% to the "modules." And when the "modules" end, the space is left blank.
This subtle change doesn't entirely "fix" the Timeline's busy structure, but it improves it a lot.