A nearby planting surrounded by a wire not electrified is usually left unmolested. Birds may be electrocuted if care is not taken when constructing the fence. Electrified fences will also keep out other pests such as raccoons, opossums, and squirrels. More information and construction suggestions can be found on Tom Clothier's pages. The issues with fencing are height and material.
Deer are very good jumpers.
Low fences sometimes are successful because they can't see a safe landing zone. That may be because the fence is solid material or because obstuctions to a safe landing are present. The threat of injury is a powerful deterrent. Injured wild animals are very vulnerable to predators and diseases and seldom survive long. Deer instictively know this.