The military term "cadre" refers to units with severe losses but intact command structures. In the game, units which are lost in battle go to a pile of cards known as "cadre". Later they can be rebuilt from cadre (represented by taking the card back into your hand). Leaders also go to cadre, when they are wounded, sacked or dismissed. In your Draw/Replace Step (Step 1), you can take any face-up card from cadre back into your hand, instead of drawing a card from your deck. Units go to cadre face-up. Leaders go to cadre face-down, and are turned face-up at the end of your next Draw/Replace Step (Step 1). Cadre is different from the dead pile, from which there is no return.
The Cadre is a DC Comics supervillain group, except for members of the Cadre of the Immortal, most of whom were redeemed and became heroes by story's end. They first appear in Justice League of America #235 February (1985), and were created by Gerry Conway and Chuck Patton.