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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. If a Pokemon uses Destiny Bond, switches next turn, and faints to Pursuit as it switches, the Pursuit user faints as well.
Grudge also involves the user fainting.