This emulates the Quartz Composer fog effect, where 3D objects fade to a set color the further away they are from the camera. Thanks to @GeorgeToledo for introducing the solution to use the depth image from
Render Scene to Image.
Edit: Joe raised an important point -- be mindful of event flow to the Fog subcomp. The cubes comp is animated so the Fog subcomp is receiving events at display refresh rate. This makes it seem like it should work everywhere all the time -- this may not be true without some attention to event flow. For example, if the Objects port only receives one event at start, may not update if you change a port setting.