Yes, you can shoot an unarmed burglar in your home, however, they have to attack you. If you discover them in your house and they are stealing your property, you can't shoot them. You may use non-lethal force to stop them. (Tackle,punch,kick, joint locks,etc.)"You can not just shoot someone unarmed for being in your house. "
As far as I'm aware of, actually you can. At least in Indiana. Someone breaking into your house is covered under the Castle Doctrine for Indiana, correct? Whether they're unarmed or not appears to not matter, as it is assumed if someone is unlawfully entering your abode, they may also cause you harm.