I do not know, but there is a fairly serious argument now out there that this could happen. It is made by Gennaro at hackermoon.com/tether-and-the-great-crypto-ice-age-115h329k , picked up on by Tyler Cowen on Marginal Revolution without comment. Among those Gennaro cites at least partly supporting his argument are Nassim N. Taleb.
So the argument is that bitcoin and most other major cryptocurrencies are now fundamentally based on stablecoins tied to the US dollar, with claims those stablecoins can be easily traded into dollars. According to Gennaro, and I do not know if he is right, the various non-stablecoin cryptocurrencies now use stablecoins to trade between each other at low costs, with these stable coins providing liquidity, but at the cost of a dangerous potential instability. If there is a rush on them, they have no ultimate backer, and a crash by them could drag all of the cryptocurrencies into an ultimate total crash into an effectively zero absorption barrier, with Taleb apparently providing some support for this possible scenario.
As it is, Tether is now the leading stablecoin, indeed the #3 cryptocurrency overall, behind Bitcoin and Ethereum. According to Gennaro, the central fact of crypto trading is that the most important ratio is that between bitcoin and tether, not bitcoin and the dollar, although the latter is the ultimate measure of value, the de facto "gold" of the cryptocurrency markets, even as bitcoin itself has been claimed to the "new gold," and gold has definitely become quite boring.
Again, according to Gennaro, a major problem with Tether is that while on the one hand it has essentially centralized Bitcoin trading into itself, if not all crypto trading. But unlike the dollar, which has the Fed to back it up, Tether has nothing. It is owned by a semi-murky Hong Kong based entity, Bitfinext, which has already been in legal trouble in the state of New York for misrepresenting and hiding certain transactions and assets. Gennaro argues this shows that it has no backing, and that a run on it will make it unable to access actual US dollars, the world's actual key currency, which could lead to an implosion dragging down the entire cryptocurrency market, given the nonexistence of any entity capable of coming to its rescue.
For those who want to find this particular tale somewhere between laughable and unlikely, while Bitcoin, Ethereum, and several other leading cryptocurrencies have suffered major declines recently, driven by such things as the Chinese government imposing serious restrictions on their mining and use, the one cryptocurrency that has gained in the last week has been, oh yes, Tether. But then pride goeth before a fall,. While I am going to stay out of forecasting anything in these markets, given how many important market manipulators are playing in them, regarding whom I have no idea what they will do, it does seem that the possible volatility and more deeply threatening threats in them has increased.