How to render objects outside the camera's view?

If you could, at least, give the code of the shader, it could be helpfull.

You will have to make some research about Frustum culling. This is the method used to not render objects which are outside the cameras' view frustum.

From the doc, it is said that :

Unity ensures that when rendering your objects those which are completely outside of this frustum are not displayed. This is called Frustum Culling. Frustum Culling happens irrespective of whether you use Occlusion Culling in your game.

See : http://docs.unity3d.com/Manual/class-Camera.html

EDIT : it is possible to modifiy the culling distance for specific layers (near and far plane distance)

I think it will be difficult to find a way to tell your cameras to render an object if it is outside the view frustum.

Oops, my bad, see this blog post :

http://allenwp.com/blog/2013/12/19/disabling-frustum-culling-on-a-game-object-in-unity/

The author simply moves the bounds of the gameobject inside the view frustum (but set the transform position back), so that the cameras render it.

 // boundsTarget is the center of the camera's frustum, in world coordinates:
 Vector3 camPosition = camera.transform.position;
 Vector3 normCamForward = Vector3.Normalize(camera.transform.forward);
 float boundsDistance = (camera.farClipPlane - camera.nearClipPlane) / 2 + camera.nearClipPlane;
 Vector3 boundsTarget = camPosition + (normCamForward * boundsDistance);
  
 // The game object's transform will be applied to the mesh's bounds for frustum culling checking.
 // We need to "undo" this transform by making the boundsTarget relative to the game object's transform:
 Vector3 realtiveBoundsTarget = this.transform.InverseTransformPoint(boundsTarget);
  
 // Set the bounds of the mesh to be a 1x1x1 cube (actually doesn't matter what the size is)
 Mesh mesh = GetComponent().mesh;
 mesh.bounds = new Bounds(realtiveBoundsTarget, Vector3.one);

Credits : Allen Pestaluky