Die Hard is a cut game mode for Call of Duty: Modern Warfare 2. It is a variant of almost every other game mode (Die Hard Team Deathmatch, Die Hard Domination, etc.). There is not much known about the Die Hard mode because it can only be played on hacked lobbies or servers.
The main feature of this mode is that the players have more chances to survive. Everyone goes into Last Stand after being shot by an enemy, even if the player's class does not contain Last Stand. While a downed player is in last stand, a teammate can revive them (a teammate in last stand is marked with a green cross). In addition, the weapons are a bit weaker than in normal game modes.
Die Hard may be a reference to the movie of the same name.
When put into Last Stand by a player, the Last Stand perk image appears, and also the message informing the player he is now in Last Stand. Sometimes, the icon and text won't show up; sometimes, a bar may appear, but this won't harm gameplay.