How get rid of shadows of meshes clipped by a shader?

My goal is to have a plane in front of which nothing is shown. Well, with some help I’ve learned that this can be done with the clipping function using a surface shader, eg. like in the clipping example in the Unity documentation:

The problem is: it doesn’t clip the shadows. So I end up with just seeing a shadow floating in thin air. How can I make the shadows clipped too?

Bit late, but if anyone else come by, use “#pragma addshadow”, and it’ll just work!