Currency failure generally occurs due to the type of hyperinflation, and there is always the potential for technical failure, currency competition, political issues and so on. As the main basic rule, there is no currency that can be considered very safe from failure and difficult times. so is it possible that bitcoin can become worthless?
Everything is possible but the question you should be asking to yourself is how likely that outcome really is? And to me the chances of that happening are very low, if there was some fatal flaw in bitcoin you can be sure that governments should have already used it and yet bitcoin is still alive which means there is not such a flaw, also bitcoin cannot be printed at will so it is impossible for bitcoin to die out of hyperinflation.
Bitcoin is also not tied to any country so even if a country falls that should not really affect bitcoin at all and when it comes to the competition bitcoin is without a doubt not only the best cryptocurrency of the world but the best currency of all that currently exist in the world so I am not worried about bitcoin disappearing or becoming worthless.