This photo shows how retaining screws can be used to adjust the "break angle" of the strings - the angle at which they cross over the nut/zero fret. While this photo shows an unfretted cigar box guitar that uses a threaded rod nut, the same concept applies to a guitar using a zero fret.
Silvertone Revolver Bass Guitar Package with Instructional DVD, Cobalt Blue
Cigar box guitar
Morris Guitar Lattice Bracing
Here is another angle of a zero fret installed on a cigar box guitar. This particular guitar featured an angled headstock, so the retainer screws are just holding the strings in the correct position, not holding them down to increase break angle.