Keep in mind that the definition of static character (as opposed to dynamic character) is one who does not change. One of the main themes of this book is the changes the war brings out in the lives, hearts, and minds of the soldiers. Paul frequently reflects on how much the war has "changed them" all. That said, Franz Kimmerich, who dies in chapter 2, could be considered a static character.
We learn from a flashback that Kimmerich is one of Paul's schoolmates, whose mother, just before they leave for the war, asks Paul to watch over her son. She is crying and carrying on, almost mirroring her own son's sensitivity and weakness. It is not surprising, therefore, that as he lays in the hospital bed, leg amputated, the others do not tell him how bad his condition is. One inference that can be made about the timing of his death, is that he was not fit for survival. His own mother seemed to know this before he went to the war, and sadly, he is one of the first of Paul's friends to die.