@Bill - Great explanation and information.
@Mr.Ohm aye God
I believe that you want to measure the motor parameters (resistance / impedance / reactance) and IR when motor is dead but motor cable remains connected. You are measuring at motor terminal with cables connected. In this condition, the measurements can done as cable is connected but open at other end. Theoretically, you should have no impact on readings obtained due to cable remain connected and under ideal conditions you should get the symmetrical results (Similar for all three phases); However, in practice,readings will be affected by cable length, routing, temperature, adjacent cables operating voltages, laying method and many typical parameters and operating conditions.
My take is use such measurements to know general health of motors while doing the routine maintenance but do not rely on them if you have to make any decisions. If you want to make important decisions related to motor condition, repair or replacement, it is recommended to eliminate all possible unknowns and variables - cable connection in this case.
NC