Elimelech was born in Jerusalem in 1974 to Billy and Avi. In her youth, she studied in a high school in Gilo. In 1991, she won the first place in Jerusalem's "Miss Kenyon" beauty pageant, and then began modeling for the modeling agency "Look". During the Contest "Miss Kenyon" beauty pageant she met the successful hairdresser David Afuta (who had many high-profile clients such as the then Prime Minister's wife Sara Netanyahu amongst others), who was 14 years older than her, and they soon became a couple.
In 1993, Elimelech participated in the Miss Israel beauty pageant and won the title "Queen of Grace" (מלכת החן).
In 1995, Elimelech received a lot of media exposure when she competed in an ongoing segment held during the Israeli version of the game show "Wheel of Fortune" during which contestants competed for the role of the new "Wheel Girl". Although she was very popular she eventually did not become the new "Wheel Girl".
In 1996, Elimelech participated in the children's video "Afrochim" (אפרוחים) together with Asi Levi, Sherry Brzezinski and Sharon Tzur. During the same year she also participated in the children's video "Golden Heart Flower" (פרח לב הזהב).
During 1996, Elimelech also starred in the TV commercials for the Israeli supermarket chain "Hiperkol" (היפרכל).
During the summer of 1997, Elimelech hosted the TV show "HaChofesh HaGadol" (החופש הגדול) in the Israeli Educational Television. That same year, her relations with David Afuta worsened and as a result subsequently she moved back in with her father and his second wife. During the same year Elimelech was supposed to participate in the annual Israeli singing show "The Festigal" with the song "Ballerina", which subsequently was performed by the participants of the Festigal in her memory after her death. On the evening of December 1, 1997, the day before her death, Elimelech appeared along with the other participants of the Festigal Dudu Topaz's entertainment show on Channel 2.
In the morning on December 2, 1997 Elimelech was found dead along with her boyfriend, David Afuta, in their home in the Ramat Beit HaKerem neighborhood in Jerusalem. She was shot once while he was shot twice.
Shortly before the murder, Elimelech's father requested the Police to confiscate Afuta's personal weapon, for fear that he might use it against Elimelech, although the weapon was never taken from Afuta because Elimelech demanded that the complaint would be canceled.
Preliminary investigations of the crime scene revealed that Elimelech was the one who shot Afuta and then committed suicide. The initial presumption, by which Elimelech was the murderer, originated on the basis that their bodies where found when the gun was in her hand. Based on these findings, Elimelech was initially buried in the suicide plot of the Jewish cemetery Har HaMenuchot in Jerusalem, in accordance with Jewish burial customs.
Nevertheless, due to pressure from Elimelech's family, during the first month after the murder the police conducted a second investigation on the case in which the investigators discovered that the original team of investigators were negligent and that actually Afuta shot Elimelech and then killed himself. It was also revealed that Afuta's brother arrived first to the scene of the crime before the police, and in order to obscure the evidence, he moved the gun away from Afuta's hand to Elimelech's hand. Although this fact was verified in laboratory tests the prosecution decided, with the support of the police, not to initiate legal proceedings against Afuta's brother and he was released. According to the findings of the renewed police investigation, during the last years of her life Elimelech tried several times to leave Afuta, but Afuta did not let her go and threatened to commit suicide if she left him and as a result she always got back to him.
The findings of the second investigation were published three weeks after the murder. Elimelech's bones were only moved away from the suicide plot of the Har HaMenuchot cemetery to the main burial plot of that cemetery during 2001, four years after her death.
In 2004, Elimelech's father and brother filed a lawsuit against David Afuta's brother Joseph Afuta, demanding that the court would formally determine that Afuta was the murderer, and demanded a compensation of 8.4 million NIS. Eventually, on 1 March 2011 justice Menachem Cohen formally ruled that the murder was committed by David Aftuta who afterwards committed suicide. He also determined that his brother, Joseph Afuta, tampered with the evidence in the crime scene with the intention of incriminating Elimelech. As a result, the court ruled that Joseph would compensate Elimelech's family with 300,000 NIS.