What is the thin flexible barrier around a cell? Cell membrane - the thin layer of protein and fat that surrounds the cell. What is a thin flexible barrier around the cell made of a lipid bilayer? The cell membrane is made up of a thin layer called the phospholipid bilayer.... Why is the cell membrane called a selective barrier? Selective permeability means that the cell membrane has control over what can... What cells maintain the blood brain barrier? The endothelial cells are the cells that maintain the blood-brain barrier. soon! Do cells enclose by barriers?