I read up some more, and I see that I've over simplified it. I like your description better. I think I must have been assuming a situation along the lines of "

I read up some more, and I see that I've over simplified it. I like your description better. I think I must have been assuming a situation along the lines of "bank loans out 90% of its deposits, and then all those debts are moved to other institutions", in which case I expect the bank would be left with 10% of its original deposits plus the loan agreements, the total value of the latter being equal to ~9x the value of the remaining deposits.