Yes, what Liberty Student said. The Treasury department and Federal Reserve will always be able to print enough Federal Reserve Notes to redeem all deposits.
You'll be able to get your pieces of paper out of the bank. There won't be any guarantee that they'll actually be able to buy anything.
The final run on the dollar will occur when people rush to convert their unbacked paper to silver or gold or other tangible goods. The price of gold will go to infinity, as people holding gold will be unwilling to trade it for paper at any price.
During hyperinflation, the quantity of money doesn't just increase. The velocity of money also increases. People with rapidly inflating paper rush to spend it as soon as possible.
I have my own blog at FSK's Guide to Reality. Let me know if you like it.