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Originally Posted by Jan-Poo
Maybe I forgot something but as far as I remember the only thing that Eua told to Satoko is that if Rika loops then she retains all memories of the loops and Satoko won't be able to undo that. This makes sense, as Rika retains the memories of the loops she experienced in the "sea of fragments" and so they transcend the single fragments she gains the memories from. So Satoko needs to make sure that she doesn't screw up and let Rika find her plot, but I don't see why it is necessary for Satoko to die after Rika.
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I think it's a rule Eua added to spice things up. If Satoko couldn't possibly fail, it wouldn't be fun.
It doesn't have anything to do with memories. Eua claimed that if Satoko dies first, she won't be able to follow Rika to the next fragment since there won't be a Rika to follow.