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If the user faints before the user makes a different move, the foe that KOed the user will also faint. If the damage occurs in the end of the turn by hail, sandstorm, Leech Seed, status, Doom Desire, or Future Sight, Destiny Bond won't work. If a Pokemon uses Destiny Bond, switches next turn, and faints to Pursuit as it switches, the Pursuit user faints as well. It will also work if the target is behind a Substitute. It will bypass Focus Sash and Sturdy. This move cannot be blocked by Protect or Detect. This move cannot be blocked by Substitute.
Destiny Bond is a move that will faint the user that dealt the last damage, the one responsible for fainting the user. It's a hard move to use in competitive battles since it requires good prediction and often surprise value to work. Regardless, it is a good move that may score a surprise KO if played right. Good users are Mismagius and Gengar, thanks to useful immunities and a high Speed stat, as they will outspeed most Pokemon and KO them if predicted right, and are also capable of doing plenty of damage before going down. Wobbuffet is also an noteworthy user that goes the opposite way; it's terrifically bulky, slow, and has a trapping ability, preventing the foe from simply switching the problem away.
Finally, Banette is a noteworthy user; she is frail and slow, but if used in the lead position, with Trick Room and Focus Sash, she can survive one hit and set up Trick Room. Since she will probably be at low health, she can use the now "faster" Destiny Bond (thanks to Trick Room) to KO the opponent while sacrificing herself at the same time and supporting the rest of the team with the field effect. This strategy is easily stopped by Taunt or a priority user, though.
Grudge is a move that also faints the user, but instead of causing the target to faint, it causes the target to lose all of its PP of the move used to faint the user.