The tiara two people wore, which will let only one of them leave the ninth floor.
The Crown is the reason the ninth floor is a trap rather than a battlefield for two of the crawl's most prominent survivors. Because Princess Donut and Katia Grim both put it on, neither can leave until all of The Naga are dead — and even once that happens, only one of them can go. Quasar delivers the mechanic and its cause in two flat sentences and adds, almost as an afterthought, "It's because they both put on some tiara."
The workaround is the Orchid of Eileithyia's Grace, the flower Huanxin Jinx and the goddess Eileithyia have arranged for Katia. If Katia takes the twelfth-floor attendant's path, Donut walks. If she does not, the Crown's arithmetic stands.
A tiara — no more is said of it here than that two people wore it and both are now bound by it.
The cursed regalia binding Donut and Katia to the ninth floor and to each other's fates.
Also appears in books you've already read — spoiler-safe to their endings: