Nothing is in the box.
What's in the box is something which drives the plot - its true substance, mass, shape, and form are unknown and unknowable.
The object in the box isn't revealed because it isn't important. It's a McGuffin.
It's like asking what was in the briefcase in Pulp Fiction. It doesn't matter, except in that it has the properties which the story requires in order to move forward.
I infer that inside the box is the ability to accept death, even welcome it. We are surrounded by a culture that mourns loss and prevents death even whent he quality of our lives will decrease significantly. The children are not scared of what was in the box and seem content with what will come if they continue to starve themselves. The father was not as close to his children and still feels the insatiable hunger of missing his loved ones which makes him empty and continually moving closer to following the same path his wife and children did.
It's like what I thought about the ending of The Sopranos (which of course frustrated the hell out off me tho, thinking about it for a couple days, I thought it was brilliant): the ending is that...there is no ending. Or rather, what is in the box will be in your mind, if you can come to a conclusion about it. In other words, the father is frustrated as hell & never learns what's in the box--just as the reader is at the end of the story. My opinion: what's in the box is something that shows you that, in the end, life is not worth living, so you may as well just "lie down" and wait for death to come sooner than later...