Offred's predecessor (who was also called Offred), is a minor but influential character in The Handmaid's Tale. She was a Handmaid assigned to Commander Fred prior to Offred's (the main protagonist's) arrival at the house. She does not physically appear, due to having committed suicide shortly before the main events of the novel, but is mentioned on several occasions. She is also mentioned in the television adaption.
Very little is known about this woman. Presumably, she was rounded up and sent to the Rachel and Leah Center to be indoctrinated when the Republic of Gilead came to power and was eventually assigned to household of Commander Fred and Serena Joy. Given she later killed herself, she may have been suffering from depression due to her dire circumstances and loss of freedom. It can be assumed she was the one who carved the pseudo-Latin phrase "Nolite te bastardes carborundorum", which roughly translates to "Don't let the bastards grind you down" on the floor of her wardrobe for any Handmaids who should come after her. It is revealed that this Offred, like her successor, was coerced into an emotional affair with the Commander and that Serena was infuriated when she found out. Shortly after, the Handmaid hanged herself from the chandelier in her room, with her body being discovered by the Martha, Cora. It is hinted that, besides finding her oppressive life unbearable, this Offred also feared what Serena would do to her in revenge for the affair, and so killed herself to spare her from the very real possibility of a slow and humiliating public execution, being tortured by the Eyes or sent to the Colonies.
As a result of the first Offred's suicide, the chandelier is removed from the room, and the glass in the paintings on the walls are removed as well to prevent her successor from attempting suicide as well. Offred finds the phrase her predecessor carved and the small act of rebellion brings her some comfort. When Offred asks the Commander about the first Offred, he reveals she killed herself, simply stating that "Serena found out" (about her secretly visiting him). The Commander seems somewhat saddened, but doesn't take any responsibility for the woman's death and it is unclear if he actually cares about the woman, or if he was more disappointed over losing his 'lover'; either way, he clearly sees the new Offred as a replacement for her, in more ways than one. When Cora finds Offred sleeping in her wardrobe, she initially panics, dropping a tray of food and screaming, until Offred wakes and assures her she's fine, Cora apparently believing Offred had taken her own life as her predecessor did before her.