Selective mesh rendering

I'm trying to create a certain effect: Imagine something ethereal coming through a wall, with only the things this side of the wall visible. Now remove the wall, but still only show the parts of the "ghost" that are this side of the wall. That's the effect I'm going for. I don't have a clue how to go about creating this effect, does anyone have any advice? Is it possible to do entirely in unity?

Some additional information that may simplify problem:

The "ghost" doesn't necessarily have to have the same lighting as everything else.
When the object is Instantiated, the area where the the object should not be rendered can be defined permanently, and can be defined as all the area on one side of an infinite plane.

 

something like cross section effect?
https://www.assetstore.unity3d.com/en/#!/content/66300

or could even add in the shader some fixed x coordinate value,
then discard (dont draw) if mypixelworldcoordinate is less than that x value

 

Thanks mgear, the first part looks like it could work very well! I'm keen to learn extra things when they come up though, so could you give me some pointers ont he second option too? Is it something I will learn naturally if I learn more about shaders?

 

this one has simple example, it changes color based on they world height position
https://www.assetstore.unity3d.com/en/#!/content/11310

similar to
https://answers.unity.com/questions/54313/shader-rgb-colour-based-on-y-value-vertex.html

 

Reminds me of the Final Fantasy Spirits Within movie spirit effects. Cool!
I have nothing else to add - other than learn up on shaders, either programming them, using amplify, shader forge or substance.