The music video for "Stay" was directed by Sophie Muller. On February 10, 2013, whilst walking the red carpet of the 55th Grammy Awards, Rihanna held an interview with Ryan Seacrest who officially revealed that the music video would premiere on E! News the following day. Rihanna described the production saying, "The video was really, really simple. I pretty much stayed put in a bathtub, and we shot it really tight, really close. There's Mikky Ekko in the video as well. This is the first time I've ever collaborated with him, so I'm excited about that because he's actually the one who wrote the song and I kinda just fell in love with it so much and in love with the tone of his voice and we wanna keep him a part of it, so you'll see him in the video." The singer added, "It's a very emotional song and it's personal, so you just think about, it's almost like telling a story, and when you tell a story, even to yourself — if you're saying it out loud and expressing how you feel — it needs to be powerful because it needs to be authentic." On February 11, Rihanna leaked an "uncut" version of the video on Twitter prior to the official premiere, featuring the singer performing to the track in one singular take, without Mikky Ekko. The official version premiered on E! News later that day. It was then uploaded to Rihanna's official VEVO account at 8AM ET the following day. Shortly after the video was uploaded, it was flagged by YouTube for its sexual content. The flag has since been removed.
The video opens with a shot of running water. Rihanna is then presented undressing and climbing into a bathtub. Throughout the rest of the video, the singer is presented nude in the tub full of cloudy green water; subtle camera angles protect her modesty. Rihanna is shown wearing little make-up and with long hair tangled and wet over one side of her face. The singer seems morose and sad as she occasionally flickers her eyes to the ceiling and puts her head in her hands, showing off long manicured nails and a diamond stud earring. The low-key video also features Mikky Ekko, who performs his parts of the song separately including scenes of him perched on the edge of a different bathtub, gazing into a mirror, in front of an unlit fireplace, and sitting on a grand chair. The video switches between the pair throughout the course of the video until it concludes with a single tear falling from Rihanna's eye as she sinks lower into the bathtub.
Eleanor Gower of the Daily Mail thought the slow moving number shows Rihanna at her most vulnerable. A reviewer of The Huffington Post commented, "The heartfelt ballad, from her latest album Unapologetic, is full of emotion - and the video matches that, as a stripped-down Rihanna soaks in a tub." August Brown of the Los Angeles Timescommented on the video saying, "we kind of want to curl up in a hot shower and have a good cry ourselves." They continued saying, "It's kind of an echo of her famous "We Found Love" video, with that clip's quick-cut, drugged-up frenzy of bad romance replaced with solitary, locked-off shots that feel more intimate than exploitative. She looks amazing, but the focus isn't so much her body as the look of constant devastation on her face." Brown summarised the clip as being "appropriately minimalist[ic]" and concluded calling it "a beautiful video that broaden's Rihanna's emotional-musical palette." Bené Viera of VH1 commented on the video saying, "Usually the tough girl posturing is a cover up for a very sensitive soul. Rihanna cut the 'I don't give an eff' attitude for four minutes of makeup free, teary-eyed, glistening wet, raw emotion in the video for 'Stay.'" Sarah Flanigan of Yahoo! thought the video shows "a softer side of [Rihanna's] personality audiences rarely get to see." She also stated, "There are no gimmicks, no flashy clothes, just a very raw and emotional performance allowing her to tell this love story in her own words." Jenna Hally Rubenstein of MTV labelled the video as "perfectly heartbreaking/emotionally vulnerable" and thought the "baptismal effect" of the video "feels like a seamless transition from Rihanna's 'Diamonds' video." Tamar Anitai also of MTV compared the video to Britney Spears' "Everytime" (2004), writing that both videos "are equal parts stunning and sobering, haunting and harrowing, and both feature impossibly famous singers reflecting upon damaged relationships while inviting us into their well-designed bathrooms as they vulnerably perform their ablutions." Rihanna's "Stay" video was also compared to and said to be inspired by Janet Jackson's "Every Time" video, as well as Britney Spears' "Everytime" video, with one critic noting "Rihanna isn't the first pop star to brood in a bathtub. Janet Jackson and Britney Spears also bared their emotion immersed in water. Janet bared all in a blue lagoon for her 'Every Time' video. A little less glam, Britney's tub scene in her 'Everytime' video proved dark foreshadowing into her troubled world."