Do points often randomly move on their own when a
signals fails to red or whatever the victoria line equivalent is?


AIUI - its in the wiring of the said point/s and signal.
The "green" proves to the driver that the points are both set and LOCKED
(safe)
However with a red signal the associated points *may*
A) Be in the wrong position (being diff to the signalmans diagram)
B) WONT be locked (unsafe) and for that reason those points "could" move as
a train passes over them (remember its a failure and with no "green" there
is no proof thay are locked). Or they may even simply be set for a wrong
route.