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This is rather minor and not even really combat applicable, but Sumireko's Dream Self should have Immortality Type 8/9 based on her real-world self:
"While the simplest plan would be to defeat her in the dream world and wait for a new dream Sumireko to manifest, for some mysterious reason she's become absurdly powerful, and ordinary methods will no longer work."
This implies that Sumireko's Dream Self dying would just cause Sumireko herself to produce another dream self afterward. However, as implied by the quote, not only would this take some time, but Dream Sumireko wouldn't keep her memories. So it's not really combat applicable but still a thing.
"While the simplest plan would be to defeat her in the dream world and wait for a new dream Sumireko to manifest, for some mysterious reason she's become absurdly powerful, and ordinary methods will no longer work."
This implies that Sumireko's Dream Self dying would just cause Sumireko herself to produce another dream self afterward. However, as implied by the quote, not only would this take some time, but Dream Sumireko wouldn't keep her memories. So it's not really combat applicable but still a thing.