Trust, or faith is the only thing that give value to every currency without a intrinsic value. That is also the case for crypto-currencies, by the way. A assumed value is not a true value.
The faith in a currency begins to fail, when the buying power of this currency decreases, especially if it decreases rapidly. That is called inflation or hyper-inflation. Once the faith into a currency begins to crumble, there is no way to restore it again. Only a new currency can get acceptance then.