There are two types of fiber, soluble and insoluble. Insoluble fiber is good for the digestive tract and soluble fiber is good for lowering cholesterol [1]. From what I understand, the liver will recycle cholesterol back into your bloodstream. Soluble fiber will bind with the excess cholesterol and carry it off as waste.
For most people it's probably okay to eat foods containing cholesterol as long as you keep everything in balance. Several years ago my blood tests showed all the bad signs - high cholesterol, low HDL, and high triglycerides. I knew I would never stick to a really low fat diet, so I just shopped the perimeter of the store, avoiding processed foods. I flipped by blood test results in two months.