This spring, Ukrainian billionaire Ihor Kolomoisky, the newly appointed governor of this region in the country’s southeast, called for building a 1,200-mile electric fence along the border with Russia to keep Moscow’s forces out.  Today he has scaled back his plans. After months of fighting that has decimated Ukraine’s armed forces, Mr. Kolomoisky is instead beefing up the defense of his province—far west of where he first proposed the fence—in case Moscow-backed militants penetrate deeper into Ukraine.