Do nema stepper motor 34 stepper motors hold the load while powered off?

If you turn off your "device" so no current is running through the stepper motor, you can use your fingers to turn the axle and feel how much force you need. You need quite little force to rotate it. Even if you don't touch the axle, it will fall out of position if you turn it off in a "non-full-step" position due to the permanent magnets (and even then it can still be a little off).

For this purpose we usually use one current setting when we move the motor and another current when it is at a halt - a hold current. The reason for this is that in full power the stepper motor can get really hot and you don't want to use the "higher" current if you don't need to. On the other hand you don't want to turn it of completely if you want to keep the exact location.

The "hold-current" is high enough to not lose the position, but low enough to keep the temperature down.

If you use a stepper motor driver, such as DRV8825 it has a reference input to "program" the current through the motor. This is usually a simple resistor divider, but with some clever use of 3 resistors you can create an extra digital control signal "Hi/Low current mode" that change the divider, hence the reference voltage and the current.

I have used this technique in direct thermal printers where you can spot instantly if the stepper motor isn't in the exact position all the time.