Anyone who is not on the border is left behind and dies.
The chance to die when being left behind is big, but they can still survive. Sorry, it’s nitpicking.
About war dogs for the player: usually you’d want to control your war dog like any other brother, right? But that’s not realistic. A dog would just charge into the enemy like an orc, which doesn’t seems very helpful to me.
I though that one brother could equip a war dog as a weapon. This weapon could have 2 skills, a normal attack, “Bite”, and “Release”. With the second skill, a war dog appears on a free hex next to the brother and attacks the closest enemy. After releasing you have no more control over your dog. If the dog survives the battle it is returned into your brothers inventory.