Losing power while the machine is moving is going to mess up your home position. The position is saved to nonvolatile memory two seconds after the machine stops so a power outage while the machine is stopped won’t cause any loss of position
When you turn the computer back on and launch Ground Control the file you were cutting and it’s position on the sheet will be saved. To resume the cut you will need to do Actions → Calibrate Chain Lengths Automatic to restore the home position. You can then use these buttons: 
to fast forward through the file until the point you want to resume.
But judging from your other post you got it worked out 
