In Missouri, you face the fence and the right half is yours to keep up, the left half is the responsibility of the neighbor. In a case where the neighbor has no livestock, they are not responsible for any fence. However, when you build the fence, you can legally take the cost of materials and labor for the fence on his half down to the court house and it will be attached to the neighbors property and if there is every any livestock on the property, that neighbor is immediately responsible for the old fence costs----that takes care of the renting later situation. In general, I believe if you have to fight about it, then you are better off to just take care of it yourself