Veins collapse when empty
Your body exists at a certain pressure, determined by your surroundings; usually, this is about 1 atmosphere of pressure, but it can go up or down (e.g. when you fly on an airplane, or when you go diving). The pressure that your surroundings put on your skin is transmitted throughout your body, and your body "pushed back" against it.

However, this means that all your blood vessels have that pressure weighing down on them along their length. Normally, when they're full of blood, the pressure of that blood will press the blood vessel outwards to counter-act this. Without the blood, however, that pressure within the blood vessel is no longer sufficient to withstand the pressure being exerted on it from the outside.

Since the walls of the blood vessels aren't thick enough to have enough structural integrity to withstand that pressure differential, they then proceed to collapse.