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The First Poisoning
The stolen child is four the first time Orochimaru poisons her; it's just a mild hallucinogen, but it leaves her shaking for hours and if she was even slightly less terrified of Orochimaru learning her secrets, she'd have babbled the whole time. Orochimaru is initially intrigued by her silence, but his attention wanders when she doesn't do anything else interesting and another one of his experiments boils over.
She has to force herself to eat, the next time Orochimaru brings her food — it might be poisoned too, but she must eat in order keep her strength up, and anyway if Orochimaru ever grows bored and decides to kill her there's nothing she can do about it, willingly eating poisoned meals or no.
Hunting
As Orochimaru's casual poisonings increase in frequency and severity, Orochimaru's snake summons prove to be the child's saving grace — sometimes they bite her, sure, but only on orders or if she startles them, and they not only offer her tips on how to survive their venom, they teach her how to handle a wide variety of other mundane and exotic poisons, including all of Orochimaru's favorites. A constrictor named Midori teaches the girl hunting; the child's patience and self-control are already fire-forged, but the skill of knowing when to strike is invaluable.
Being able to supplement her diet by hunting for food which she can be reasonably certain isn't poisoned lifts a weight off her shoulder that the girl hadn't even realized she was carrying.
In Oto
Oddly, the poisonings die off once Orochimaru founds Otokagure. Orochimaru has a whole village to torment and experiment on now, and if he ever actually succeeds at poisoning her fatally then he'd have to run the place himself instead of just delegating all the tedious tasks to her.
That does unfortunately leave her as eight year old in charge of a village full of snarly, dangerous ninja who resent taking orders from a literal child instead of their charismatic, deadly new kage — she needs every advantage she can fabricate, so now it's her turn to poison people.