Theoretically, in the event of a power failure at the input, nothing should happen, because this is a normal operating state, when, for example, you decide to turn off the device with a switch on the input, so I don't know what the concerns are.
If it's a typical buck, it has a transistor in the power path, in these times it will be a mosfet on the bank. If so, it has a diode in the structure that will transfer the output voltage to the input (taking into account the diode drop). Until the whole thing goes below the UVLO, the converter works almost as normal, only the falling voltage will force it to a large fill ... except that we have more at the output than at the input, so this keying will do little more than reducing the drop on the diode with the open channel of the transistor .
It would be more interesting to plot VIN against VOUT in this case. Because they are feeling, the VIN should follow the VOUT, once with a decrease in the diode, and once without, due to the open transistor.
), there is nothing specific there except a tiny MLCC. Maybe someone took the executive circuit's catalog note too seriously, where they are usually understated on "marketing pages" and only somewhere further mention that larger ones are recommended? 
