When the helo is in auto, there is no torque applied to the main rotor! Therefore the airframe cannot yaw in the opposite direction to the applied torque. In the event of a total tail rotor failure, (a) the tail rotor will either have gone! or (b)have stopped, TR auto doesn't exist! There is consequently no friction effect.
When selecting auto after a tail rotor drive failure the a/c will recover some of the yaw induced by the malfunction(i.e. the yaw in the opp direction to the rotation of the MR). Then, when the engine(s) is/are stopped, this corrective yaw will increase (in your favour), though probably not sufficiently to allow you to be pointing in the direction you wish to go!. At the bottom of the engine off manouevre, when you flare like ****, the corrective yaw will again increase, substantially this time as the rotors speed up and the airframe (thru friction effect) yaws in the SAME direction as the main rotors. It is this rapidly developing change in yaw that one should strive to take advantage of to offset as much yaw as possible prior to cushioning the touchdown.. In reality because of lack of experience/judgement, 99% of all helo drivers will be unable to align the a/c fore and aft, and must therefore attempt to wash off ALL fwd speed (zero spd landing)prior to touchdown. Otherwise you will cart-wheel!!
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Thermal runaway.