The answer was hard for me to figure out because you need to put together clues that occur at three places in the book, and if you miss just one, it doesn't really make sense.
When Carla is talking with Viridian's son, Boone, he says:
"She had such a complicated relationship with men. ... its a power struggle, because of course they tried to control her, too, and you could argue that a lot of the time they did, or maybe the world did. Her writing. Her career. It wasn't fair and she knew it."
Shortly after this conversation, Carla thinks:
Sometimes things come to you, it seems like out of the blue. But your brain's been working on the problem all along, you realize later, some underpaid-file-clerk portion of your brain, taking notes and writing reports. Maybe it was Boone telling me that Viridian didn't trust men. Which I already knew, or assumed, knew at least that she resented the power they'd had over her. She'd told me as much. She'd trusted me enough to tell me.
She would have had a plan for the poems. The plan hadn't allowed for incapacitation.
Or maybe it had.
Earlier, when Viridian was in the hospital, worried she was dying and somewhat mentally confused, she told Carla:
"Read A Defence of Poetry," she said. "That's Shelley. Very important."
"All right," I said again.
"It's difficult but I have confidence in you. Now don't disappoint me."
"I won't," I said, although I didn't know how to avoid disappointing her or anyone else.
Putting everything together, Carla realizes that maybe she was the only one Viridian trusted enough to tell where the poems were hidden—men were out, and other poets were out. So Carla thinks back, recalls the conversation in the hospital, and realizes that maybe Viridian was giving her a clue. So she goes to Viridian's house, finds Viridian's copy of Shelley's A Defence of Poetry, an old book with heavy leather covers, and discovers the poems hidden beneath one of the covers.