The fear is that higher interest rates would damage the economy. The problem with that worry is that the Federal Reserve could buy bonds itself, to cancel out the foreign selling.
The hidden assumption is that this selling would have to be very rapid. If the foreign reserves managers liquidated their Treasury holdings over five years (for example), the selling would be easily absorbed by other bond market particpants, and nothing much would happen. So, we have to imagine concentrated selling over a span like a week, and the foreign reserves manager is for some reason unconcerned about the price (yield) it sells at.
The question asks: how would they sell? That is the real issue. It is very difficult to see how such sales would represent the national interest of those countries.
If the foreign central bank sells their Treasury bonds, they end up with US dollar cash. They need to do something with that cash. What can they do with the US cash?
- They could buy risk assets (equities, real estate) in the United States. However, countries generally do not want to buy too large positions in risky assets with their foreign currency reserves, and they would face questioning by the US government if they tried. In any event, US risk asset prices would rise, and everyone in the business press would happy, not panicking. Not a plausible option.
- They could buy commodities (or goods). This is equivalent to blowing all their foreign currency reserves to buy imports. If there was a global scramble to buy commodities, such an outcome is possible. However, to do this all at once would be expensive. They would more likely want to spread purchases out over time, so that they do not drive up the price of whatever they are buying. (Furthermore, if they buy oil, the dollars would go to oil producers, who would likely reinvest back into dollars.)
- They could buy other foreign currencies (third party countries). The problem is that few countries have the capacity to absorb a huge wave of inflows, and their currency would become very strong versus the US dollar. (The euro is the only plausible candidate, and most foreign reserves managers already own a lot of euros.) The involved foreign country could get mad, and freeze the assets of the foreign central bank that is moving into their currency. Countries diversify their foreign currency reserves, but try to avoid causing disruptions.
- It is possible that entities in the private sector want to sell their local currency, and buy US dollars. For example, we see wuch behaviour during financial crises. The foreign reserve manager would lean against this, selling US dollars to buy back their local currency. This effectively creates a shift between the reserves portfolio (which sells Treasurys) and the private sector portfolio (which is buying US dollar assets), and the net effect on the Treasury market is ambiguous. However, the usual response to a financial crisis in the Treasury market is for yields to fall (e.g., LTCM Crisis, Financial Crisis).
- If they buy their own currency, and the are no corresponding capital outflows, their currency would get extremely strong, and/or their trade balance would have to shift into a deficit. If they buy their currency, someone has to sell. This counter-acts the reason why they have US dollars in the first place - to keep their currency cheap, to develop their export sector. (For example, see the discussion of the “Bretton Woods II” system - [link to NBER paper by Dooley, Folkerts-Landau, and Garber] 1.
In summary, it might be possible to find a scenario where such sales make sense, but they probably require something else to go wrong for the United States. Something has to cause foreigners to want to dump their dollar holdings, without worrying about their own trade position.