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If the user faints before their next move, the Pokémon that fainted the user will faint as well. This does not take into account any end-of-turn damage, such as hail, sandstorm, Leech Seed, status, Doom Desire, or Future Sight.
Arm Thrust, Barrage, Bone Rush, Bonemerang, Bullet Seed, Comet Punch, Fury Attack, Fury Swipes, Icicle Spear, Pin Missile, Rock Blast, Spike Cannon, and Twineedle do not activate Destiny Bond.
Grudge also involves fainting the user.