Is it possible to break the bones in the top of your foot from foot hyperextension?

Sure its possible: Forceful hyperextension is common in an automobile accident, sometimes from a fall injury and usually the rearfoot bones are more affected, but it is certainly possible.

Yes: If you have a traumatic injury where the foot is pointed downward, this can cause an avulsion fracture to the top of the foot. Severe downward pointing injury core abuse a more involved fractures and/or dislocation. See your foot specialist. Dr l.

Yes: Yes, this type of injury is called a lisfranc's fracture/dislocation. It is often missed whih is unfortunate because treatment is necessary. Arthritis can occur down the road with or without treatment but outcomes are improved with treatment.