He means that the price of the bonds backing the mortgage fall.
Since the bonds are fixed interest, when interest rates rise, new bonds at a higher interest rate are more profitable than the old bonds at a lower interest rate. As such the free market price of the old bonds will drop to until the selling-at-a-loss reaches an equilibrium with the expected increased profit from higher interest rates of the new bonds over the lifetime of the bond.
This lets the loan taker buy back their own bonds for less than what they were paid (the loaned amount) when the bonds were issued.
Say a bond was originally worth say $100 and generated $10 of income in time T (10%). If interest rates rise so that $100 will now generate $20 (20%), then the original bond is worth less to a buyer. If we ignore the time delta, that bond would only really be worth $50 ($50 to generate $10 is the same 20%), so it's half as valuable. (The time change would bring it somewhere in between, depending on how long has elapsed).
This lets the loan taker buy back their own bonds for less than what they were paid (the loaned amount) when the bonds were issued.