That could be impossible to happen, Bitcoin is International digital currency and as digital banking system the paper money will be valueless. Bitcoin no need to print on paper, with in next few years the paper money destroy by bitcoins.But if someone would try to do that government and local authorities will sue for that because it is illegal and not be done by any other individual in state and real printed dollars.
When Govt prints too much currency then inflation happens. Though it is not the only reason for inflation. However it is one of the major reason for inflation. Good examples is look at the strongest currencies in this world. US dollars, British pound, Bahraini Dinar, Euro are some example. Their supply is very limited and highest denomination currency is less than what most other countries have.
Next point about everything in economics has value only because people collectively have perceived it so. Thus When govt rejects or stops recognition of legal tender of the currency-note then that note will become worthless piece of paper. Bitcoin has value because people are perceiving and accepting the value supported by it. No govt can stop it. At max they may block bitcoin. Till there are groups of people who perceives value in bitcoin it will remain as valuable.