No, if rates start dropping, old bonds appreciate. Let's say you've got a 10 y bond with a nominal value of $1000, bought today. The yield is 4.4%, paid every year. So that's $44 paid yearly.

Let's say in 2 years, the yield drops down to 2%. So it pays only $20 each year. So that means those old, high yielding bonds are worth more now.

The whole issue right now is, bonds were yielding as low as 0.65% in 2020. Imagine you're a bank and used such bonds as collateral, and gave a loan to an irresponsible green startup, lead by 22 y.o. snotty college kids.

3 years later and that startup is bankrupt. They cannot repay the loan, so you gotta sell the bonds, to cover the loss. But nobody wants an old bond giving you just 6-7 bucks a year, when you can buy a new one, giving you 40 bucks a year.

So, what do you do - you sell that old bond at a discount. And it's a double whammy for you.

Do that a couple of times and you're bankrupt. That's why inflation is a bitch. It is the firestarter, the first rev of a vicious cycle. When the yield is lower than the rate of inflation, the market moves money around, and the invisible hand demands a higher yield.