Once the host exhausted their own physical strength, they could no longer suppress the malice lurking within the Cursed Seal.
In the manga, when Sasuke Uchiha fought Itachi Uchiha, he exhausted every means at his disposal and depleted his chakra. That was why Orochimaru's Cursed Seal on the back of his neck went out of control, becoming so unstable that Orochimaru was reborn directly from it. After all, even when Kabuto Yakushi poisoned Mitaraishi Anko into unconsciousness, the same Cursed Seal on her body had never gone that far out of control.
Although White Zetsu had drained Hanabi Hyuga's chakra, he had only taken the surface layer of physical energy she used for everyday activities. She was nowhere near as utterly spent as Sasuke had been under Orochimaru. However, Hanabi did not constantly guard against and suppress the brand power between her brows the way Sasuke had with Orochimaru's Cursed Seal. Secondly, Wu Yu's use of senjutsu chakra was far superior to Orochimaru's twisted approach to sage cultivation, which had never allowed him to truly master Sage Mode. Thus, while Hanabi Hyuga was unconscious, Wu Yu's will within the brand between her brows could release its power directly, conveniently allowing him to speak to Black Zetsu as Gray Mysterious.
Black Zetsu, possessing Hinata, fell silent for a moment.
Gray Mysterious, possessing Hanabi, asked, "What's wrong?"
Black Zetsu spoke hoarsely through Hinata. "It seems that in the future you came from, the bitter lesson of being sealed away again truly left an indelible mark on Mother..."
So much so that she had considered defeat before victory. On one hand, she had sent Gray Mysterious back into the past to join forces with him and prepare to turn the tables. On the other, she had also had Gray Mysterious leave behind the