Combine the beer and brown sugar in a small saucepan over medium heat, and cook, stirring occasionally, 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.
Serve on its own or on your favorite sandwich roll.
The beer can be from a can or bottle, and you can use whatever you usually drink or keep on hand. I've made this with everything from Miller Lite to Lebatt, Guinness, Heineken, you name it! They all work just fine.
The brown sugar can be light or dark.
The sauerkraut can be from a can, jar or bag - just make sure you drain it well.