It's not that the dollar would have long-term instability, it's that the act of going from reserve currency to non-reserve currency would see people in other countries dumping dollars for whatever the new thing is. There would be a short period of hyperinflation in the US.
That doesn't mean it's going to happen, but if it did happen, it wouldn't be nothing.
Hyperinflation is a monetary phenomenon. USD sales by foreigners wouldn't be sufficient to cause hyperinflation. Who are they selling to, and for what?
Foreigners hold a large number of US dollars, as reserves. If the dollar stops being the reserve currency they want to stop holding it as reserves, so they trade dollars for something else. The new reserve currency, other hard currencies, real estate, stocks, whatever they can get. The market gets flooded with dollars and the dollar drops against other currencies.
Americans with mortgages and other debts are happy to take US dollars they can use to clear their debts and foreign buyers are happy to get US exports for their declining dollar holdings, so the foreign dollars would end up in the domestic market and cause hyperinflation.
That doesn't mean it's going to happen, but if it did happen, it wouldn't be nothing.