Max was a dog who appears in Alan Wake.
Max is a dog who was injured by a bear trap from poachers in the woods. When you first check in to the cabin he will be laying on a table with his paw bandaged by Rusty.
Later on, when Rusty is hurt inside Elderwood Visitor Center, Max is in a cage to Rusty's right. When he is carried away, barking is heard and upon returning, Max will be lying just outside the hole in the wall, dead.
If you talk to Rusty, he says that the dog got caught in one of the bear traps. This foreshadows the fact that the player will be encountering the same sort of traps when they go into the forest.
After Rusty is attacked and before Alan Wake leaves to turn on the lights, you can walk up to the dog's kennel and Alan will say "Shh. Good boy".