I actually made a reddit post 2 weeks ago about if it was possible to create a decentralized banking system: http://www.reddit.com/r/Bitcoin/comments/240n26/decentralized_bitcoin_bank_possible/
But what if there is a run on the bank, lets say bitcoin went down to $100 from $500 and everyone wanted to withdraw their bitcoins at the same time, the bank wouldn't have the equity.
Just like the bitcoin network has a protocol for transactions this banking network would have a protocol for issuing the debt. You can set the required collateralization to the desired level for each respective network as easily as you change the block reward on a bitcoin fork. Bitshares is already creating a decentralized bank and exchange with 200% reserves. There is a lot more information at bitshares.org and bitsharestalk.org.
I don't believe that this system is impervious to bank runs even though it does not use the fraudulent fractional reserve system. If markets are not efficient and there is a run on the bank then ppl will lose money. But this is true of any banking system as we will soon see in the US when interest rates adjusts and banks default again.