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?
Maybe bitcoin will be worthless if there's no people wants to use it and if the value of bitcoin will gone. But as of now no one can say if bitcoin will be worthless because if you see the price now is continously to grow so its hard to determine if bitcoin will be worthless in the future.