The liver stores and produces sugar, or glucose, depending on the body’s need. During a meal, the liver stores glucose as glycogen for later use when the body needs it. The high levels of insulin and suppressed levels of glucagon during a meal promote the storage of glucose as glycogen[1]. If a person with diabetes does not take insulin, the pancreas may not be able to respond effectively enough to rises in blood glucose. As a result, the liver may not be able to take up glucose from the blood and store it as glycogen[2]. However, the liver can still make sugar when needed, such as during periods of fasting. The liver supplies sugar or glucose by turning glycogen into glucose in a process called glycogenolysis. The liver can also manufacture necessary sugar or glucose by harvesting amino acids, waste products, and fat byproducts[1]. Therefore, if a person with diabetes does not take insulin, the liver may not always be glycogen depleted, but it may not be able to store glucose as glycogen effectively.
Citations:
[2] https://www.diabetes.co.uk/body/glycogen.html
[3] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3753545/
[4] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5481557/
[5] https://8fit.com/fitness/glycogen-depletion-signs-symptoms-and-working-out/
[6] https://www.hopkinsmedicine.org/health/conditions-and-diseases/glycogen-storage-disease