Since circumstances have changed I will repeat my suggestion that was previously "modded".
In my experience aircraft can only fly TO an FMC fix. Now, as a pilot in an aircraft west of Indonesia who wishes to fly the aircraft on an unlikely track for a long enough period of time to ensure it runs out of fuel what fix position would you enter into the FMC to meet these needs, a fix position that requires no great imagination. Obviously the geographic South Pole.
If anyone is taking bets I would locate the aircraft on a track from its last known position to the geographic South Pole and a distance along track to a little beyond the last Inmarsat ping.