Well... The bank could start with half a billion, and lend $450,000 of it. Then whichever bank that gets put into could lend 90% of that again, and so on. After a few times, there's a billion dollars lent from half a billion.
I fail to understand your reasoning: 0.5e9 * 0.9^n < 0.5e9 < 1e9. In other words: No one is ever receiving $1B even if banks' balance sheets sum to more than $1B lent collectively. On par, each bank is holding a small part of the 0.5e9, and then the final individual is holding the rest.
So? If you chain the loans, the bank might have the final balances: ($50M, -$450M) and ($45M, -$405M) and ($405M). The bank's net loan after settling internally is still $500M. Even if spread across banks, the sum of "real" money loaned out is still only $500M. If the loan at the end of the chain defaults, the loss is only $500M net.
