What happens when you leave a broken ankle untreated? Will it heal by itself?

Painful ankle. The outcome of a broken ankle depends on the severity of the fracture and displacement of the ankle joint. A simple nondisplaced fracture may heal without any treatment but many other fractures required immobilization or surgery to prevent further pain, deformity, and arthritis.
The bones will heal. The bones should stabilize however probably not in the correct position. This can lead to limited range of motion, chronic pain and arthritis.