Last time there was a run on a Chinese currency, the central bank stood behind the HKMA and said the territory had the full backing of the central government.This is not just a problem for Taiwan but a issue for the entire world as the USD weakens people are losing money on their USD denominated investments. So there is pressure to sell those asset which lead to further weakening of the USD which leads to more selling. It becomes a vicious cycle. The weakening of the USD is making investing in US assets less attractive for foreigners just as the US need to roll over 7 trillion dollars of debt this year. Its not going to be pretty. The USD is weakening because of the massive amount of debt that the US is carrying but also because of Trumps policies. The US cannot afford to raise interest rate as that would collapse the asset bubble's and make the big debts unpayable.
So America is stuck because the economy is under pressure from two opposing forces and there is no solution for it. You try to solve one problem you will exacerbate the other. America will either end up with a massive deflationary collapse or hyperinflation you can pick you poison.
I'm sure this time would be no different... the mainland is ready to back Taiwan with RMB