This instant death trick is available only for Halo: Combat Evolved.
Just after the first cutscene in the Pillar of Autumn, you begin you de-thawing from a cryo-tube. Right after you jump out of the "hushed casket", jump on the tube so that you are under the Cryo Tube's cover.
When the cover closes, you will be pushed "through the ground" and "fall to your death".