That space is in fact empty. You would need to make a solid in that space in order to give that region material properties. If you make another solid body inside and de-select "merge result" you will end up with 2 distinct bodies which you can apply different materials to.
This is basically how you'll have to do it. If the box shape is very complicated and you can't just fill it with a simple extrude then you can use the following method to get a solid body of the inside:
1. Before you shell, make a copy of the solid body.
2. Shell the original body.
3. Make a copy of the shelled body.
4. Do a combine-subtract to remove the copy of the shelled body from the copy of the unshelled body.
This will leave you with the original shelled body and a body that fills it.
You could also use the Intersect tool.
1) Make a copy of the shelled body
2) Create a plane or surface representing the filled level
3) Use the Intersect tool to create the filled portion
Oh that is even easier, unless maybe there are a lot of openings that would need to be covered.