An open circuit (broken wire, disconnected terminal) will be 0.0mA
2 wire loop powered transmitters use up to about 3.5mA to power the sensor electronics. Any controlled value below 3.5mA is unrealistic, since the device needs power for operation.
NAMUR specs define a fault or fail-safe failure mode at something around 3.6-3.8mA. The people who pay attention to NAMUR frequently calibrate an input to see 3.7mA (or 22.3mA on the high side) knowing that that's indication of a serious fault.
Poor calibration or the use of a non-precision dropping (shunt) resistor (say 233 ohms, rather than 250 ohms) on the analog inpt can produce apparent values below 4.0mA.