Possible causes of a loan decreasing in price in secondary, alongside a decrease in yield?

That can only be possible for putable or callable bonds, and other complicated financial instruments that may combine different types of derivatives or stocks and bonds (convertible bonds). This has nothing to do with the recent extremely low interest rate environment or index floors.

Putable bonds are bonds where the issuer can sell the bonds back to the issuer, which gives the investor protection against bond losses. Let's say interest rates keep on rising, causing bond prices to fall. Once the bond price reaches the floor/strike value of the bond, the bond will not lose anymore value because the investor is guaranteed at least the strike price of the put option.

Callable bonds are bonds that can be called by the issuer at par, and are expected to be called if the price goes above par. Let's say interest rates fall, the value of the bond will rise. However, because the bond will be called once the price exceeds the par value, the price of the bond will not exceed 100.

To sum it up, for putable bonds an increase in interest rates can only cause the value to fall down to the strike price of the bond because of the protection provided by the put option. The reverse is true for call options.