Anchor one end of an unrolling plane

I have created a plane and attached a bezier curve modifier.
I am trying to animate a roll of steel unrolling, and I need the starting edge to stay anchored to the edge of a plane which sits below the roll.
The problem I am having is that when I move the plane or the bezier curve to simulate the steel unrolling the end that needs to stay in place slides back as the steel unrolls.

Any help would be appreciated.

If the end slides back animate it moving forward to compensate for this movement