I'm working on an idea and it might sound a bit far-fetched but it is a 'virtual currency' made to be stored offline much like a paper wallet. But I'm not storing any bitcoin private key. I'm creating what is called a ticket. Each ticket has a unique set of codes and the whole idea is that it must be easy for people to write down these codes so you can create your own set of money or complementary currency. A long story short, my plan is to use Bitcoin as an "intrinsic value". Since the whole point of this project is mimicking physical cash in a cashless society 
it can't be backed by fiat.
it can't be backed by fiat. The problem with this is that it'll be easy to brute-force the codes since you would be making it easy for people to write it up and keep it as it is. Moreso, like what franky1 said, offline paper wallets are good for storage of value but not so much when we talk about circulation. You'll likely have to come up with a solution to make offline paper wallets easier to circulate without the use of internet, or very little use of it so as not to expose your codes on these tickets.
Another point to make is that the idea is that small or large communities can run their own server backing their 'community currency' and it doesn't have to be that powerful. It is not a decentralized solution, so it will be built on trust, but there is no way to trace or log transactions, just like cash.
In other words, you will likely be a bank since you will be handling the issuance of such tickets and the servers are needed for watch-only purposes? Trust is pretty much a hard thing to come up with these new ideas, especially if it's something connected with money and the concept of it. Ripple made it out alive and expanded since it has the budget to market itself as something different, but for this project, it will pretty much be a steep slope to climb.
Add to that fact that this might be illegal since you will be creating your own "money" and you will be issuing them. Better check for legal implications first before continuing with this plan.
As a community currency you don't need to trade your ticket for bitcoin for each transaction, but if you don't want to create your own set of cash, you can burn a ticket for a new one and also (in the future) collect it's value ..
I'm keen to know on how would you implement such, knowing that no records of transactions and ownership whatsoever would be created for your cash.
I'm glad I started this discussion. I have learned a lot. After some search, three words keep showing up. FinCEN,CVC and Money Transmitter . I think my idea of using Bitcoin as an intrinsic value to back each ticket could complicate things.
I will continue working on this project. I might be the last person laughing after all WTSHTF 
. As John Wick would have said it -Everything's got a price