From this report two things emerge. First, there is such a thing as Pole of Inaccessibility, in this case, the Southern one. Second, Ilyich has found its way there.
Quoting the wikipedia about the station:
Today a building still remains at this location, marked by a bust of Vladimir Lenin that faces towards Moscow, and it is protected as a historical site. Inside the building there is a golden visitors' book for those who make it to the site to sign.
All that's missing from a "proper" geocache is a trinket exchange box.