Combine the beer and brown sugar in a small saucepan over medium heat, until the sugar melts and the mixture is slightly thickened; set aside.
Cut the kielbasa into links and place in a slow cooker. Cover with the drained sauerkraut. Pour the beer and brown sugar mixture over top. Cook on high for 4 to 6 hours, or on low for 8 to 10 hours. (We ended up doing a combination – high for 3 hours and then low for another 3 or so. Definitely the longer it cooks the better it tastes!)
Serve on its own or on your favorite sandwich roll.