How can anorexic people still lose weight if their metabolism is slow?

Starvation. People with anorexia nervosa limit their food intake to the point where they're literally starving their bodies. Along with many other issues, there is loss of all fat stores and muscular wasting. This happens in other starvation situations also, such as concentration camps and being prisoners of war. In these, though, the food limitations are coming from external controls.