Maybe you were confusing perspective with depth? There is no such thing as a "perspective-correction" of shadows.

Perspective is caused by a projection from a point. You can see this with shadows in real life. Shadow lines move a little outwards and a shadow on a wall is bigger than the person that throws this shadows. This is the same in a 3D engine. The dynamic lights that cast volumetric shadows are just points in space. When the light source is far away, like the sun, the perspective is barely noticeable.

"Depth" means that far away parts of the shadow look more blurry because they are outshined by the environment light. This requires several shader passes and affects the frame rate, so most 3D games don't use this effect.