She is portrayed by Jennifer Jason Leigh, who also portrayed Daisy Domergue in The Hateful Eight.
When Alison "Allie" Jones posts an advert request a new room-mate - following her split with cheating boyfriend, Sam - a last possible candidate for the vacancy turns out to be Hedy (as Allie nicknames her).
After a successful interview, Allie eventually lets Hedra move in: however, things aren't as they seem with Hedy.
When Sam calls - hoping for reconciliation with Allie - Hedy erases the message he leaves on the answering machine. She later buys a puppy (that she calls Buddy) which she pretends is a stray, so she can bond Allie.
After Allie decides to go on a date with Sam, a moody Hedy sits alone in the apartment watching TV - and violently kicks Buddy away, when he sits by her feet, pining. Later, when Allie and Sam go out again, Hedy throws Buddy out of the window - where he dies, after hitting the pavement way below - and blames Sam, by making out that Buddy was able to jump off the balcony, because Sam was unable to fix a loose railing.
Allie later finds that Hedra has clothes that are identical to hers, in her wardrobe - and is appalled when Hedy's "surprise" for her turns out to be Hedy getting her hair redone to match Allie's. Hedy says that she did this, because she thinks of her and Allie as sisters.
After Mitchell Myerson (Allie's new boss) tells Allie that, if she doesn't do as he says, then he'll warn off future clients - before he then attempts to rape her - Hedy later learns about it, and phones Myerson. Pretending to be Allie, she threatens Myerson, by telling him that if he does anything, then he and his family "are fucked!".
Later, Allie finds a shoebox in Hedy's room, which contains letters that Sam wrote to her (that Hedy hid from her) and newspaper clippings - which reveal that not only is Hedy's real name Ellen Besch, but that her (Hedy's) twin sister drowned when they were nine years old.
Allie then decides to follow an oblivious Hedy to an underground sex club, where she witnesses Hedy pretending to be her. When Hedy arrives home, she overhears Allie confiding in her gay friend Graham about her fears about Hedy.
Furious, Hedy duct-tapes the air-vents (through which sound travels between Graham's apartment and Allie's apartment) and attacks Graham, after sneaking into his apartment.
Afterwards, she visits Sam (whilst pretending to be Allie) and forces herself on himself. When Sam decides to tell Allie about what happened, Hedy panics and kills him - by stabbing him through the eye, with a stiletto heel.
The next day, Hedy - who has been furiously cleaning the apartment - tells Allie that she is leaving. Allie sees the news report of Sam's death - and figures out the truth, before then trying to leave the apartment, as well.
Hedy reveals her intention to frame Allie for killing Sam, since people think she and Hedy look so much alike. She also tells Allie that Sam forced himself on her and came in her mouth, so she killed him out of self-defence.
Hedy ties up Allie in Graham's apartment, and leaves the TV on for her, whilst she goes out. However, whilst she is out, Hedy gets a phone call from her father - so, she flees back to Graham's apartment. There, she finds out that Allie has turned up the TV volume so loud, that there has been a complaint about it. She tells the people outside the flat door that she is watching the place for the weekend - and that the flat is on a timer.
She then storms inside, and slaps Allie for betraying her trust.
When Mitchell Myerson arrives, looking for Allie, he follows Hedy to Graham's apartment. When she asks him who he is, he says his name - and she tells him that she knows no one called Allie. However, when Myerson sees that she is carrying a case belonging to Allie - before then hearing a scream from the flat - he pushes Hedy aside and runs into the flat.
There, he finds Allie bound and gagged - and lying on the floor. When he attempts to free her, Hedy knocks him off of Allie with a gun she is carrying and - using a cushion as a silencer - kills Graham, by shooting him in the head.
Later, after Allie pleads with Hedy "don't make me leave you", Hedy thinks that Allie has come to recognise her place as Hedy's twin. However, Allie is caught out, after she tries to send a round-robin e-mail saying she needs help.
Hedy then tries to force Allie to take her life: first, she forces Allie to type up a suicide note; then, she places Allie's hand on the computer monitor, so that people will think she wrote it; and then, holding Allie at gun-point, tries to get Allie to overdose.
However, instead of complying with Hedy, Allie smashes the glass of water in Hedy's face - before then fighting her down to the ground, cutting Hedy's arm with a glass shard from a broken window pane, and then running to the front door and prising it open.
Hedy then comes running out with the gun, pleading with Allie. However, Allie states that she is no longer Hedy's sister: but rather, she is now like Hedy, in terms of having lost a sister. Graham (who has just come round, at this point) comes out of the bathroom and tackles Hedy to the ground.
When Hedy points the gun to Graham's head, Allie grabs her by the feet and drags her out of the apartment - and, as she is clinging to the door, Hedy accidentally traps her fingers in the door.
A struggle then ensues - which ends in the elevator, after Hedy strangles (but not kill) Allie. Down in the basement, Hedy then starts looking for means to dispose of Allie's body.
However, after she finds Allie has gone, Hedy then looks for her at the back of the basement. When Allie throws a rat down onto Hedy, Hedy then goes to where she thinks Allie is. There, she actually sees Allie - and follows her into the boiler room. However, when she sees Allie's shirt sticking out of the wardrobe door, she thinks Allie is there - and then opens the door and attacks what is actually her own reflection in the mirror.
Allie then comes down - after having hidden above Hedy - and stabs her from behind. Hedy falls to the floor before the film shifts to her apartment room getting cleared out as Allie's voice-over narrates the closure. Her final fate is left ambiguous, as it is never shown or stated outright if she lived or not.