The Soviet rouble, and the Latvian rouble before the LVL currency established.
Just curious, will you still have access to your stocks if the Internet collapses?
I'll still technically own them, but I'll have to access my broker (which is located in my own country) by some other means, i.e. telephone, mail or physically showing up at their office. About 50% of my stocks are owned through a very large fund, which mainly operates by mail anyway. I guess the stock exchanges themselves will at least attempt to stay open in such a scenario; it will probably be chaos but the stock market is at the basic level just a list of orders, which could in principle be sorted manually. Or at least without an internet connection. But you'll still own your stocks as long as there is a paper trail _somewhere_, worst-case you might not be able to sell them for a while.
If the internet became unavailable for a long time, it would be a very interesting situation regardless...during a calamity like that, you might be better off having all your money in real estate or other physical goods.