USD will go down in hyperinflation, but it might be the last one standing.
Bitcoin might be too late to come as an alternative. Depends on bitcoin usage expansion and the timeframe of USD fall.
The PTSB (powers that shouldn't be) might think up an alternative fiat some time in the future. It could even be a centralized fiat cryptocoin.
Here is a fun fact from the money history. (I couldn't be bothered to find references for this now, do it yourself or disregard it as a fairytale). At some point in time and space, the currency was so debased (think silver coins with a low silver content), that a single coin bought almost nothing. It was custom to use a bag (purse) to hold a number of coins, and exchange the bag. The receiver would not normally open the purse to count the coins, because he knew that the next person would also not open it. Therefore the fact that the number of coins could be one or two short of the standard was not important.
This is analogous to the fact that some dollar bills are fake, but you don't check each bill thoroughly, because you know that the next guy doesn't either.
Now the point of this long story: The bitcoin network does not have to be available to everybody at all times, for bitcoin to be universally useful. Fixed amount of coins, like bills, could be created on a sheet of paper with the secret under a fold. This could be used as money, and someone accepting it could check if he wanted. Else anybody could just accept it and hope that most of his bills are loaded. The issuer could even date and sign it for later reference.
So yes, bitcoin could be useful money for everybody in case of an epic fiat fail.
The value would of course also rise epically.