This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
In 3064, the Khi'eth was on a mission to investigate a "dilithium nursery" in the Verubin Nebula. During the mission, the ship crashed on Theta Zeta, located at the center of the nebula. The Khi'eth's distress signal was picked up by the Federation starship USS Hiraga Gennai, which communicated that it would take two weeks at maximum warp to reach their position and offer rescue. Having heard nothing from the Hiraga Gennai, the Khi'eth presumed it was destroyed attempting to penetrate the nebula's radiation storms.
Six months later, Doctor Issa sent a distress signal which was broadcast on all channels. She described the crew's emotional state as being hopeful, even though they were stranded and they had not heard from the Federation since the Hiraga Gennai's destruction. The apparent radiation burns on her face suggested that she might be suffering from intense radiation sickness; (DIS: "Terra Firma, Part 1") however, Saru recognized Issa's facial markings as a sign of pregnancy. Su'Kal, born to Issa after the crash, was left alone in the wreckage of the ship, with a holographic environment (created by the dying Issa) to sustain him. (DIS: "Su'Kal")
In 3189, using data gleaned from the black boxes of three starships and the experimental program SB-19, the point of origin for the melody was discovered by an engineering team aboard the USS Discovery. Paul Stamets and Adira Tal wrote and ran a signal transmission restructure algorithm to find and decode the message within the signal. After successfully decoding the signal, it was determined by the team that they had recovered most of the message, save for the ending which, despite their best efforts, proved difficult to fix. The message was later presented to Captain Saru in his ready room. (DIS: "The Sanctuary", "Terra Firma, Part 1")
With the broadcast of the distress signal in a loop, it was surmised that the ship had some structural integrity and that its systems were operational. Saru ordered the engineering team, who had the prefix codes to the onboard sensors, to get back door access to those systems, so they could see what was happening aboard the ship.
A little while later, the engineering team attempted to hack into the Khi'eth's systems by using the long-range sensors. Although initially unsuccessful, because of their weak signal being unable to pass through the static at the space-subspace barrier, their effort ultimately prevailed when Cleveland Booker loaned them his range extender allowing them to overcome their difficulties and get a signal that held to the Khi'eth's systems. The Discovery began the process of recovering data from the Khi'eth. (DIS: "Terra Firma, Part 1", "Terra Firma, Part 2")
The recovery of data led to the discovery of a life sign, the aforementioned Su'Kal, within the crashed Khi'eth. The Discovery traveled to Theta Zeta and found the Khi'eth's structure to be intact. An away team, consisting of Saru, Michael Burnham, and Doctor Hugh Culber, were beamed into the starship. They found themselves in the world created by Issa, with their outward appearances changed for the sake of Su'Kal. During the course of their investigation, the team came to learn that The Burn had been accidentally caused by Su'Kal himself, when he emitted a powerful psychic shockwave. (DIS: "Su'Kal")