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Offred wasn't allowed to work anymore because she was a women. Her card didn't work because it was no longer valid, anything marked with an F rather than an M was invalidated and frozen. The new laws read that women couldn't work and couldn't own property.
The Handmaid's Tale
Offred lost her job because she is a women and Gilead have changed all laws to favour men not women. They froze women's bank accounts at the same time too to prevent women from leaving Gilead. Gilead still needs women to make babies and be home workers such as Handmaids and Marthas.