Brown the sausage in a skillet, breaking it up into small chunks as you cook it, and spoon off the fat. Drain the sausage on a few layers of paper towel and allow to cool.
Beat the cream cheese in the bowl of a stand mixer with the paddle attachment until it is fluffy.
Mix in the Swiss cheese, sauerkraut, and sausage, mixing in between each addition.
Set up a dredging station with the eggs, flour, and breadcrumbs in separate shallow bowls. Whip the eggs with a fork until well-mixed.
Roll 2-tablespoons or so of the sauerkraut-sausage mixture into a ball - your hands are going to get gooey. Roll the ball into the flour to coat it evenly, then roll it in the egg and finally in the breadcrumbs. Press down lightly to make sure the breadcrumbs stick. Set the breaded ball on a plate and repeat until all the balls are done.
Refrigerate the balls for about 30 minutes or as long as overnight. This will help the breadcrumbs stick.
Heat the oil to 350-360-F in a cast-iron or heavy-bottomed skillet. You want the oil to come at least halfway up the sides of the breaded sauerkraut ball. A digital meat thermometer can help you get an accurate read on the oil.
Carefully add the breaded balls to the hot oil - working in batches, so you don't overcrowd the pan - and fry them for 2 minutes or until golden brown on one side, then carefully flip them over and fry another 2 minutes or until golden brown.
Transfer them with a slotted spoon to paper towels and sprinkle with salt.
Cool the balls for a few minutes, then dig in!