Superman and the remaining inhabitants of the merged DC universe were introduced to the second Supergirl in the three part "Supergirl Saga" that ran in the Superman comicbooks of September-October 1988 (SUPERMAN #21, ADVENTURES OF SUPERMAN #444, SUPERMAN #22). Her appearance is foreshadowed in SUPERMAN #16, as a mysterious woman clothed in a Super uniform is found frozen in the ice in the Arctic. Once again, another parallel Earth hidden away in a "pocket dimension" was threatened and needed the aid of Superman. On this Earth, Superman had started his superheroic career as Superboy, but had disappeared 10 years earlier and left his world without a superhero. Now evil Kryptonians were invading this planet and its defences were weakening. Lex Luthor and his wife, Lana Lang, fought bravely to oppose them, but Lana was killed and the world seemed doomed without a superhero. In honor of his wife and in memory of Superboy, Lex created an artificial, shapeshifting lifeform named "Supergirl" based on his wife's form (her molecular matrix to be specific) and imprinted her with Lana's memories.
The stage was set for another historic meeting of Superman and his female counterpart. The fledging superheroine travelled to Earth Prime to bring back Superman in hopes that, together, they might defeat the supervillains. But in the battle that followed, her world was destroyed and she was left its sole survivor. Greatly injured from the battle, Superman brought Supergirl back to his Earth and left her with the Kents to recover. Soon she would strike out on her own, but it would take some years for the new Supergirl to truly find herself.
Between the 3-issue origin miniseries and the modern Supergirl series that began in 1996, this Supergirl - or "Matrix" as she called herself - had a special (Supergirl & Team Luthor), a four-issue 'Supergirl' miniseries, and ongoing guest appearances in the Superman comics. For a while she mistakenly took up with the evil Lex Luthor II (actually Lex Luthor in disguise), believing him to be like the Luthor of her world. Eventually she discovered Luthor's true nature and took off (in the 1994 miniseries). She drifted, a superhero without a purpose or a base. The memories of her original planet faded, and she found herself a superhero with no secret identity and few real ties to her adopted home. Matrix faced the existential crisis of a superhero without an identity - a creation of men, she struggled to find her purpose in this world. Luckily, Kara's spirit lived on (while Crisis had killed the bodies of many Silver Age heros, it has been noted that their souls continued to exist). Kara had found another Linda Danvers and become her "guardian angel". Matrix had the superpowers, mission and form of Supergirl, and Linda had the heart and spirit of the first Supergirl. Together they would become whole.