The Death Crystal is a magical stone that any forest monster or Master may use on you, provided it has successfully damaged you for at least 1hp. You can't lose your horse during a player duel, online or offline.
Your enemies only get to use this weapon if you are riding a horse. Which is lucky for you, because the crystal's entire purpose is to kill you, but your horse always intervenes, dying in your place. After your poor valiant steed is vaporized, you "pummel your enemy with blows". Usually your enemy will then be dead. Sometimes your enemy will still survive, but with 0 HP. One more attack of any sort will finish him off.
Any time you take damage in battle while in possession of a horse, you have a 1 in 27 chance of losing your horse to a Death Crystal. No matter what you are fighting, if the monster pulls out a Death Crystal, you will automatically kill it immediately afterward, whether it be Rude Boy or the Red Dragon itself (which results in a horse kill)