What is cheap material that absorbs water in packaging? I am thinking cheap material that can be used between two layers of carton that absorbs water. 
I want to use air but I still think that there may be other materials available that


absorb water
can be easily removed when the outer carton layer is damaged


Possible materials


carbon (well absorbing)
air (cheap and easy)
sand (should be bad)


What is cheap material that absorbs water in packaging?
What you are looking for is most probably silica gel.
http://en.wikipedia.org/wiki/Silica_gel

It is a highly water absorbent material with large surface area. It is often used in packaging as well as in laboratory in desiccators. 

You can actually buy it packed or in bulk easily (let me not link explicit offers here). You can regenerate used (old) silica by heating / drying / pumping, so you don't need to buy every single time new one if the old gets less effective.