In datasheet for the 2380, pg 3 Specifications, it lists the minimum operating voltage.
Suppose you have the 2380-500-15 model and using the low current range (3Amps), the min operating voltage is 0.6V at 3Amps. It increases to 4.5V at 15Amps for the high range.
This means when operating in CC mode and pulling 3Amps, the 2380 will develop a voltage drop of 0.6V between the HI to LO terminals. Think of the 2380 as using the output stage of a FET to control the CC mode.
This voltage drop could be attributed to the I*Rds of that FET plus other I*R drops in the path inside the 2380.
Consequently, your device that is supplying the current cannot have a voltage potential lower than this minimum operating voltage of the load. The load needs to be able to develop at least the minimum voltage drop in order to maintain the CC set point.
In situations where you want to test your device at voltages lower than the minimum operating voltage, use an external (linear) power supply in series with your device. One floats on the other.
Use the remote sense lines to still measure the voltage only from your device rather than device + external supply.
Otherwise, the entry of the max and min voltages during CC mode should be influenced by the I*R drop and open circuit voltage of the device that is suppling the current to the load.