I see no viable reason why other currencies should necessarily fail as well if the dollar is going to kick the bucket. All major currencies are not tied to it in a way that would make such conclusion meaningful. Why Euro or Swiss franc should fail if the dollar dies? In my view, they will only get stronger due to the dollar demise. Euro will be the first to take the place of the dollar as the main world reserve currency once this place becomes vacant.
I agree that many countries, for example, China and Russia, keep their reserves in dollars. But these reserves consist not only of dollars. Both China and Russia are also net buyers of gold. Besides, as far as I'm familiar with the question, the dollar reserves roughly match national debts of these countries denominated in dollars. So even if the dollar collapses, their dollar debts will evaporate as well.
Therefore it won't be a great loss for them.