Many diabetics are also hypertensives. They are prescribed apart from hypoglycemics (for controlling high blood sugar ), medicines to lower blood pressure. the commonly prescribed medicine to lower blood pressure is Beta Blockers. These act by slowing heart rate and reducing the force of heart beat. Apart from its action on heart ,it also has some effect on other organs including liver.
When blood sugar falls liver converts stored glycogen into glucose and pumps into blood. The beta blockers block this action leading to hypoglycemia.
The most commonly drug used is Atenolol. It is a selective beta blocker,hence its action is confined mainly to heart and as such has very negligible effect on the liver.