Granny used to have her act together, as both a caregiver and a contributor to Ember's society. Lina remembers that "Granny's shop had once been a tidy place, where each ball of yarn and spool of thread had its spot in the cubby holes that lined the walls […] Granny unraveled sweaters and picked apart dressed and jackets and pants; she wound the yarn into balls and the thread onto spools, and people bought them to use in making new clothes" (2.15).
Lately, however, Granny has been letting the shop get messier than messy. This is because "Most days, she just dozed behind the counter in her rocking chair" (2.16). The result is that everything is crazy mixed up and hard to find: "Long loops and strands of yarn dangled out of the cubbyholes, and the browns and grays and purples were mixed in with the ochres and olive greens and dark blues" (2.16). It's clear from these descriptions that Granny has let herself and her shop go a bit. And by a bit, we mean a lot. She's so flaky these days, that she even fails to keep a eye on Poppy, who, at the ripe old age of two, can't quite take care of herself just yet.
Lina's upset by how forgetful her grandmother is, as our narrator tells us, "More and more, her grandmother's mind seemed caught in the past. She could explain the rules of pebblejacks, which she'd last played when she was eight […] but she would forget what had happened the day before yesterday" (4.19).
But Granny does remember some stuff, such as the fact that something—who knows what?—is lost. When Lina asks what it is, she replies, "I don't quite recall… Something important" (4.5). Whatever it is, Granny's tearing apart the apartment trying to find it, looking inside of sofa cushions and in every possible storage area. And whatever it is, her grandfather (the seventh mayor) had been talking about it before he died. That's enough information for it to stick inside Granny's head as something important that needs to be found, even if she has no idea what it actually is.
As Granny continues to tear open their apartment to search, the box actually turns up, but she doesn't know it yet. When she falls ill, she asks Lina: "Did we find it?… The thing that was lost… The old thing that my grandfather lost… " (10.13-15). She's got a pretty persistent mind, for someone so scattered.
And that turns out to be a very good thing. When Lina answers that yes, they found it, Granny "sank back onto her pillow and smiled at the ceiling… She coughed a couple of times, closed her eyes, and fell asleep" (10.17). Not long after this, she passes away during the night. But she manages to hang on long enough to make sure that the box, which is essential to the survival of the citizens of Ember, lands in the right hands. We have no idea if that's what she meant to happen, but who cares? As long as Lina's got the box, there's hope for Ember yet.