Rihanna began working on the new sound for her seventh studio album in March 2012, even though she had not yet begun recording. During the production of the album, several musicians and producers were recruited including American singer Mikky Ekko and producer Justin Parker. According to Ekko, the production of the album was massive, "Their pace is insane. They had the studios we were working in booked out for three months, on a cycle. It was like nothing I had ever experienced before. "Stay" was written and produced by Parker, Ekko and Elof Loelv. Initially, when they wrote the song, Ekko didn't like it because of its vulnerability; however, collaborators convinced him to listen to "Stay" again. After another listen, he understood that the song is very important to him, "The track had become so special to me as well, and knowing what the track means to me and what I think it means to her too.

Shortly after Rihanna's management took over the song, Ekko met her in Los Angeles where she told him she already sang the vocals, on which he reacted positively. Rihanna's and Ekko's vocals were recorded at two recording locations by three different people: Mike Gaydusek at Nightbird Studios and Marcos Tovar and Kuk Harrel at Westlake Recording Studios, both in Los Angeles. Vocal engineering was done by Gaydusek and assisted by Blake Mares and Robert Cohen. Vocal production was completed by Kuk Harrell. It was mixed by Phil Tan at Ninja Club Studios in Atlanta, Georgia. Additional production was performed by Daniella Rivera. "Stay" impacted the United Kingdom on January 7, 2013 as the second single fromUnapologetic. In the United States, "Stay" was released to contemporary hit radio and rhythmic radio on January 29, 2013, as the third single in the country following "Diamonds" and "Pour It Up". It was released as a CD single in Germany on February 15, 2013.

"Stay" is a pop and R&B ballad that consists of piano and guitar instrumentation. It is written in the key of A aeolian, a natural minor system, having the chord progression of C-Dm-Am-Am₇. The song has a moderate tempo of 112 beats per minute. Rihanna's vocal range in the song ranges from the low note of A₃ to the high note of E₅. Greg Kot for the Chicago Tribune described the song as being "stripped-bare". The lyrics revolve around "failing to resist true love", according to Dan Martin for NME, as Rihanna sings "Funny, you're the broken one/ But I'm the only one who needed saving." According to Jocelyn Vena for MTV, Rihanna "punctuates the emotions of the track" on the lyric "It's not much of a life you're living/ It's not just something you take [it's] given. Rihanna also makes a plea to her lover, singing "'Round and around and around and around we go/ Now, tell me now, tell me now, tell me now you know/ Not really sure how to feel about it/ Something in the way you move/ Makes me feel like I can't live without you/ it takes me all the way/ I want you to stay. Lewis Corner for Digital Spy wrote that Rihanna's vocals glow over the simple yet effective piano riffs.

As part of promotion for the release of Unapologetic on November 19, 2012, Rihanna premiered "Stay" on Saturday Night Live on November 10, 2012. She also performed the album's lead single "Diamonds". Rihanna performed a solo version of "Stay", without guest vocalist Ekko. Rihanna wore a Bob Marley dress and adorned red lipstick. Jocelyn Vena for MTV praised the singer's performance, writing "Rihanna used her touching vocals to prove that not only can she sex up a performance but she can also sing the heck out of one. Erika Ramirez noted that Rihanna "belted out the song.

During the seven days prior to the release of the album, Rihanna embarked on the 777 Tour, a seven-date promotional tour where she performed seven concerts in seven different cities in seven different countries across North America and Europe. Not included on the set list at the first concert in Mexico City, she performed "Stay" at the second concert in Toronto as part of a medley with "Love the Way You Lie". The solo version of the song was performed the third concert in Stockholm. At the fourth concert in Paris, it was performed as the ninth song out of 13 in between "S&M" and "Where Have You Been", preceded by a snippet of "Take Care". The fifth and sixth concerts were held in Berlin and London, respectively, where Rihanna performed "Stay" both nights in between "S&M" and "Unfaithful". The seventh and final concert was held in New York City, where "Stay" was also performed. Erika Ramirez for Billboard attended all seven concerts as part of the press committee, where she described the audience as being in a "trance" as the singer performed the song.

Rihanna performed "Stay" at the final of the ninth series of The X Factor on December 9, 2012. Once she had finished performing the song, it transitioned into an acoustic version of "We Found Love" followed by the original version. Rihanna wore a short white dress, with white T-bar shoes, diamond earrings and matching silver jewellery. The singer performed "Stay" together with Mikky Ekko at the 2013 Grammy Awards on February 10, 2013.The performance featured the singer standing in front of a "dimly lit set" and was dressed in a long "curve-hugging" dark dress. Mikael Wood of Los Angeles Times positively reviewed the performance and wrote that it was the most memorable moment of the night. Charley Rogulewski of Vibe in a review of the rendition wrote, "Her [Rihanna's] beautiful voice took center stage during the duet, assuring those watching why she was worthy of her six Grammys". A reviewer of Capital FM wrote that Rihanna looked visibly moved by the performance as she showed her "impressive vocals". The solo version of "Stay" is included as part of the set list on Rihanna's fifth headlining concert tour, the "Diamonds World Tour", as the twenty-seventh track and first of the encore.