A person without one big toe would still be able to balance himself while walking, jogging or running. The big toe does play a crucial role in standing upright and moving, but a person could still move freely without a big toe after he got used to his new gait.
The big toe is responsible for bearing nearly 40 percent of the weight of a person. It also pushes off of the ground each time a person takes a step. For these reasons, if a person doesn't have one big toe then his gait may be slower, shorter and choppier than a person who has all ten of their toes.