Simply nothing, it doesn't matter which next paper currency is going to rule the world the only thing does matter is the variation of KING (bitcoin) in the cryptocurrency market. It is also possible that after the downfall of USD, bitcoin will gain more popularity because of a major shift from the USD to other currencies, and may be people would prefer bitcoin at that moment.
Dollar is indeed a different market entirely even though it is still somehow intertwined in the crypto world being a currency and since bitcoin's value is being tested against the dollar. However, with people saying that crash in USD will affect Bitcoin simply shows how ignorant they are.
In the worst case scenario that dollar is even losing its value in the market, just like you said, attention just like we are seeing right now will be focused on bitcoin and people will find solace instead and that of course will even make the value of bitcoin to keep rising. However, a fall is normal and for those trading the Forex market, understands that better.