There are a variety of conditions that can cause both low white blood cell count and low hemoglobin. These conditions are generally serious and require monitoring by a doctor.
Cancers, especially blood cancers like leukemia, can cause significant damage to the blood. As a result, both your white blood count and hemoglobin count are lowered.
Some cases of anemia are caused by a decrease in blood cell production in bone marrow. In these cases, both your hemoglobin and your white blood cell count will be low.
Chemotherapy treatments, while effective at treating cancer, can also damage blood cells and result in decreased hemoglobin and white blood cell count.
Autoimmune diseases cause your immune system to attack your own body. Many can also result in damage to the blood, leading to a low hemoglobin and a low white blood cell count.
Nutritional deficiencies can also result in a low hemoglobin and low white blood cell count.