Some argue that Alberich *is* killed in the final apocalypse, we just
don't get to see it on stage. In a recent production in Stuttgart,
Alberich was killed on stage. But it has become fashionable in many recent
performances to speculate that Alberich *is* the only survivor, and that
he is plotting to steal the gold yet again...in other words, the stealing
of the gold is a sort of 'eternal recurrence' in which events are doomed
to repeat themselves throughout eternity. 

In the Barenboim/Kupfer 'Ring', before the music starts, the curtain opens
on a full stage, and Alberich is lying on the stage in the forefront. The
other characters soundlessly depart, then the music begins, and when it is
time for Alberich to enter the scene, he simply stands up rather than
entering from offstage. When we reach the conclusion of 'Götterdämmerung',
Alberich arrives on stage just as the gold is returned to the
Rhinemaidens, and then he ends up in the exact same spot where he is at
the beginning. Presumably the figures on stage at the beginning of 'Das
Rheingold' were the participants in some earlier 'Ring' cycle. In other
words, Alberich is the linking element between an infinite series of
dramas in which Alberich fights to obtain the gold. The Chicago 'Ring'
also used this idea, as the last image on stage is of Alberich and a group
of Nibelungs under his control manipulating some sort of ring-shaped
device. 

J.K. Holman summarised the fate of the dwarf as follows: "Alberich is
last seen at the end of [Gd II-i], having urged his son Hagen to
persevere in the plot against Siegfried.  Alberich has said that if
Brünnhilde ever returned the ring to the Rhine Daughters, then 'no ruse
could ever retrieve it'.  Alberich presumably no longer poses a danger
but he is the only major character to survive and whose whereabouts at
the end is unknown.  One doubts that his ambition and hatred are
quenched."