If the target creature dies but that card leaves the graveyard before the persist ability resolves, it won't be returned to the battlefield
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I'd never played anything like it in Modern before
Let's say a player plays a game and never draws his awesome Dragon
Loots cheap to cast, and if we can stuff the deck with other cheap nonland permanents (oh, like that Senseis Divining Top!) we can effectively dig through our library for a spell to cast each turn and hopefully re-ramp ourselves back up to a serviceable amount of mana before our opponents can
However, there are better options for similar effects such as Tainted Remedy for life gain prevention or Grafted Exoskeleton for a more aggressive approach, so Everlasting Torment may not see as much play in competitive decks but could still be a strong choice in certain metagames or casual play