How is it possible that my blood sugar high when I haven't eaten?

Insulin deficiency. Even for people with type 2 dm, relative Insulin deficiency is the reason blood sugars go up. When fasting, your body has to be able to respond to the Insulin you make in order to stop the liver from making its own supply of glucose. If one is Insulin resistant or has undertreated type 1/type 2 dm, there isn't enough Insulin to turn the liver's glucose production down- it causes hi fasting sugar.