Die with the Swap broom enabled, and choose "No" at the continue prompt. Young will wake up in his apartment, and you will see the treasure chest.
Alternatively, you can get the card from DRAWER (see page for directions on how to enter Drawer).
Once inside Drawer, follow the path of bodies until you reach a room with 2 warps.
Take the one on the right.
You are now on a small island. Follow east until you see a pier. Reach it with swap and go to the north east corner of the small island. Swap one screen north from there and you should be on a second pier. From the most northern point of the pier, go west to reach an island. Continue north then west on a smaller one. You should see black squares to the left. Go there and the card is yours.