What changes occur in an anemic person's body, making the body absorb more iron from the food?

Complicated: When patients become anemic, there is an increase in iron absorption proteins (metalothionines) in the upper small bowel to increase the avidity of iron absorption. Ordinarily, heme iron (in meats) is better absorbed than nonheme (vegetable sources, including beans) and is less affected by other factors like vitamin c, fiber content, oxalates. Medicinal (inorganic) iron is not affected by these.

Change in hepcidin: To over simplify, hepcidin is an acute phase reactant produced in the liver that is important in iron regulation. Depending on the cause of anemia- in iron deficiency- hepcidin will be downregulated resulting in the increase intestinal's absorption of iron from the food. In anemia of chronic disease-hepcidin is upregulated and as the result- iron absoprtion of the GI tract actually decreases.