What's the mechanism that prevent glucose concentration dropping too low?

Hormones: Called counter regulatory hormones tend to resist the severe drop of bs. Such hormones include cortiol, Epinephrine and growth hormone. You also have the liver act as a reservoir of glycogen that can be broken down into glucose in times of need such as acute hypoglycemia or during prolonged fasting.

Without diabetes : In generally healthy people, glycogenolysis takes glycogen (stored glucose) and converts it back to glucose when the body needs it. Gluconeogenesis takes Amino Acids from the body to make glucose during a long fast.