A little thought will reveal the answer to what happens. Since the earth is not flat but frisbee like, when you get to the start of the rounded part, it begins to rotate under you at the exact rate that will make you think that you are still on flat ground and since the universe is infinite you will continue walking this rounded section while continuing to believe that you are still on a flat earth, which will reinforce your sense of a flat earth as the whole time the disc continues to rotate at the exact rate that reinforces your sense of a flat (or more correctly, a disc shaped) earth and at some point on your travels of the rounded edge the flat earth will begin to rotate at a 90 degree so that you now walk not only over the arc but not also at an angle perpendicular to the edge curve of the disc, thus creating a retrograde movement to further reinforce your belief of a flat earth, which is based in no small part by the experiments of the brave investigator who managed to fly almost 2,000' in the air in an outstanding effort to disprove the entire body of science that has evolved over the last 2,000 years, during which time no one has managed to successfully fall of the edge.