Select Inverse Points of a Shape and Delete

Bryan,

As I see your image, you wish to also have a line under each letter corresponding to the flat bottom segment; for that you can (after having everything deselected) ShiftClick each of the flat bottom segments with the Direct Selection Tool, then Ctrl/Cmd+C+F, then moving them vertically by the desired amount, then switching from Fill to Stroke with the desired Stroke Weight and Cap style (Round or Butt).

You want to create the letters so they are flat on the bottom with a line under them like in the picture.

First Expand the letters.  You can do this under Object.  Then UnGroup them.  Then with the Pathfinder Tool.... use the Minus option.

Now for each letter you will need the same rectangle.  So just make a few copies for each letter.  The rectangles can be as long as the word as well.  So this way you do not need to move them around.