Neck Vein Narrowing. If you are referring to pathological narrowing, it can be the result of previous clots damaging the vein, prior catheter placement in the neck vein damaging the vein as the result of scar tissue, or because of a prior phlebitis. Non-pathological visible "collapse" of the neck veins seen externally on the skin can be caused by dehydration or certain positions (veins collapse when lying down).
More info please. Need more information to give a detailed answer to the question.