****** SPOILERS *******
I'm not sure which shack you mean but after a night in a motel after the Vagrant picks up the girl from prison, they burglarize a house and have sex in it. Also, using clothes and guns they find in the house, they get dressed up. The Vagrant keeps pulling out the gun and "fake" shooting it as if he's a gunfighter. However, the last time he tries that the gun accidentally goes off and the bullet ricochets back and hits him above his left eye. He doesn't appear too badly hurt, but it does affect him some. After they leave the house, they backtrack to the original site of the NoDak's (Nate's) broken down pickup truck and are confronted by a police roadblock. They are investigating the NoDak's death by freezing. The officer allows the Girl to see the NoDak's ID, and after recognizing the name and address, she realizes the man (the Vagrant) she is sitting next to is not the man she communicated with while in prison. She says nothing, and they are allowed to continue along the road. She begins to confront the Vagrant and gets out of him that he killed the NoDak. After a bit, the Vagrant's car also beaks down and because he no longer has his trailer attached, he has no way of fixing the car. He says they'll freeze to death. She declares that they are not going to freeze to death sitting there, so she forces him to get out of the car and start walking. After a short way, and near a church, he can no longer walk. They are sitting there in the snow, and she tells him a story that some woman told her about the settlers in that area who got stuck in the snow did not want to die alone. She implies they are in the same boat. He asks her if she loves him. She says no, gives him a small gun to presumably kill himself, then she walks away toward the church. Even though she stumbles, the implication is that she lives and the Vagrant dies. Roll credits!
Hope this helps even though it's been some time since you asked the question.