Over the last few years, the amount of currency is circulation (and the corresponding liability on the Fed's balance sheet) has been growing; however, the asset side of the BS hasn't increased. By basic accounting, that means one of the other liabilities (either required reserves or excess reserves) has been shrinking.
I'm guessing the growth in currency volume has been offset by declining excess reserves, but I don't understand the mechanics of that. Does the fed send $100 bill to a bank and then reduce that banks' excess reserves by 100 dollars? If so, how does the Fed decide which banks' account will be reduced by how much?