In your case, you should have gotten a servo/stepper with brake for Z axis.
It is a hardware feature, so software can not help, but if the loop is closed in LinuxCNC at least it will know the position.
PCW's idea with enabling fast after fault and if loop is closed in LinuxCNC is very good.
As for your question, drive fault will disable the motor in the drive, so nothing LinuxCNC can do about it (except above), and so will LinuxCNC disable everything when it gets a fault error.