Falconer dies in Chapter 27, the very last chapter in the book.  The chapter in question opens with Falconer engaged in a duel with Mr. Armin.  At first, it appears that Falconer will surely emerge victorious, as he drives "Mr. Armin backward first one step, then another".  Falconer at one point "step(s) forward and thrust(s) at Mr. Armin's unprotected chest", pierching his doublet and dealing him a painful but not serious wound along his ribs, but when he withdraws to strike again, thinking to catch Mr. Armin off-guard, Mr. Armin performs a crafty movement which allows him to inflict a fatal blow.  Mr. Armin falls forward under Falconer's blade, thrusting his sword before him parallel to the ground.  He catches Falconer with his sword "squarely in the belly", and Falconer falls, mortally wounded.

Although Falconer seems "less like a man in pain than one who is simply unutterably weary", it is obvious that his life is slipping away.  Before he dies, he pulls away the very authentic mask which covers his face, revealing his true identity.  Falconer is really Mr. Bass, Widge's master and the man who ordered the young boy to steal a copy of Shakespeare's play.  A talented but frustrated actor, he had hoped to stage the play using his own performing company (Chapter 27).