Imagine you wanted to start a bank, so you create a cooperation and issue  1 million shares of stock to the shareholders.  On the date the bank is formed, it has no capital.

Now imagine that there are 1000 shareholders, among them are cunicula and bytemaster.

Now imagine that cunicula would like to sell some of his equity in the bank in exchange for USD, so he advertises that he would like to sell 100 shares for 1 USD.

Now imagine that someplace else in the world, bytemaster would like to borrow some USD from the bank.   This bank is no fool, and demands collateral for the loan.  Fortunately, bytemaster has some equity in the bank and offers to put a lean on it to back his loan.  The bank agrees, and issues bytemaster brand new USD Notes which are an IOU from the bank.  Now the bank is not dumb, it makes sure the collateral is worth at least 2x the value of the USD note it gave bytemaster because the bank now has a USD debt on its ledger. 

Bytemaster sees cunicula's advertisement and decides to sell the USD Note to cunicula in exchange for his shares in the bank.   Now cunciula knows the bank is solid and is holding plenty of collateral backing its Notes and so he accepts the USD Note from cunciula and deposits it into his savings account at the bank where he earns interest on his deposit.

Time passes and eventually bytemaster pays off his loan or the bank seizes his collateral to cover the loan. 

A little later, Charles comes along with the USD Note he received from cunicula when he sold his car.  Charles decides he would like to invest in the bank so he puts in a bid to buy the bank's stock with his USD Note.   If no one in the market is willing to take the bid and the bid is above the margin threshold, then the bank will step in and redeem the USD note to purchase $1 USD worth of stock.    The bank could do this because it has plenty of collateral.

Now I believe everyone can agree that if this were a real bank and the bank stock has a non-0 value that each and every transaction would be valid and 'safe'.   The USD note's from the bank would have a market value of about 1 USD and the purchasing power would be defended by the bank which would honor its IOUs.   There should be no doubt that the USD would track real USD even though the bank never had any USD on deposit, only offsetting ledger entries and collateralized loans.

So take this system that works in a traditional corporation manned by real people operating for a profit, and replace it with a blockchain.   The only thing the blockchain needs to know is the market value of USD relative to the bank's stock.  Fortunately, there is a reliable way to get that information:  always pair every individual who wants to borrow USD with someone who wants to buy USD.    Then have the borrower pay interest to the buyer.  The bank acts as the middle man and takes a cut on transaction fees and match making.   Of course, the borrower and buyer must always agree on the price and neither will bid more or ask less than what USD is worth. 

So, buy this simple analogy, I hope I have shown that the BitShares system is really no different than existing banks except that instead of issuing new USD with your house as collateral, it issues new USD with the bank stock as collateral.