Winnower could have just given her some power for entertainment or as another potential tool in her argument against the Gardener. Or like Archival has said....maybe Winnower doesn't care about the Hive at all and for shits and gigs, it showed Eris how to beat Savathun.
Eris has no Ghost or Light left. Maybe she made a deal like those other Guardians that went into The Black Garden.
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She is still Considered Light Born. She just lost her connection to the Traveler. But I think because she lost that connection, the Darkness will spare her, like it did with Mara.
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<The Darkness didn't have the time to blow apart the Awoken, the raw Dark/Light energy saved the Exodus Green from their demise. Also it was Alice/Alis that made the neutrality call, not Mara, who was nobody at the time.>