That's not how it worked in free banking, what you had is what you had and if you emitted more currency than others are willing to hold you lost your gold, then your interest bearing items, (stocks, bonds, annuities, loans may have to be sold etc.) if that was not enough then it is the physical assets of the bank, and then if all that did not cover the outstanding issue then each stockholder was liable, as there was unlimited liability for the stockholders, for what is left in proportion to the amount of stock they owned.
So all of that kept over issuing to a minimum. An additional thing that kept depositors from suffering losses was after all of the above happened the other banks would step in and buy up the outstanding notes at par. Over it's 13+ decades in existence there were very little depositor losses.* It was the very best of banking systems.
Our neighbors to the north had free-banking as well, and suffered none of the panics in the 19th century that the US did and got through the Great Depression without a single bank failure.
So get rid of the Fed and all that comes with it and these bad issues go away. No reserve requirements, no government provided deposit insurance...all of it just gone. And we can stop worrying about it in the same way we don't worry about our national food policy. Or socks or ammo or any of the other things the market brings to use on a daily basis.
This is a good intro into the history of the beginning of the Fed and a contrast and comparison of banking in (mostly unregulated) Canada vs. ( the heavily regulated)** US during the 19th century. The book linked above is excellent and a google search will lead to more. http://www.youtube.com/watch?v=JeIljifA8Ls
This is main blog of those at the forefront of going back to free-market currency and banking. http://www.freebanking.org/
* It stopping being really free in 1845 with Peel getting his National Bank Act passed. Though there are still a few banks that issue their own notes. There are a few note issuers left in N. Ireland and Hong Kong as well. There were more than 60 countries that had free-banking but I have not seen the full list. Sweden and Chile had free-banking so that's seven, I'd love to know what the other countries were but the info is behind the Jstor paywall and in books that I cannot afford just yet.
** There was a more unregulated banking system in the US in New England called the Suffolk System and not surprisingly it worked quite well.
And that is probably more than you wanted to know!