During the design process I was thinking about how the box might be open in different ways. This led me to adding a kinetic element to the inner chamber of the box that might hold the tissue.
Here the sliding motion of the handles to open the box would lift the inner holding chamber that contained the tissue up and out of the box.
I felt this not only added the benefit of bringing the tissue in and out of the box without intervention but also conjured a more secure feeling for the user as the tissue would be simply placed on the tray and carefully lowered in and, when opened, out of the box by the box itself.
A hard porous tray and a flexible net like holder are two possible systems.