DC Motor Coil Voltage
Stepper motors have very high inductance, which opposes current change and limits how fast the motor can be stepped. By raising the voltage and adding external resistors in series with each phase, the L/R time constant is reduced so the motor can step much faster. In effect the external resistors make the current draw almost constant, whether the motor is stepping or holding position. 

However using resistors wastes power, so advanced controllers apply PWM which uses the winding inductance itself to control current. The PWM ratio can also be varied to tune speed and torque to the load. 



Whether the controller uses resistors or PWM to control current, voltage read across the windings with a DC meter will be much lower than the supply voltage. If your controller is a resistor type then you could connect your solenoid across one stepper phase and its associated resistor. However the extra resistance and inductance of the solenoid could affect stepper operation, and might even damage the controller. 

You should use a separate circuit to power the solenoid. If you want it to operate in synchronization with stepper operation then either monitor the input commands to the stepper controller or develop a signal from the phase voltage waveform, then use it to operate the solenoid driver.