If I recall correctly, what happens to Alyssa is not explicitly mentioned in Final Fantasy XIII-2. This is, however, explained in the book Final Fantasy XIII-2: Fragments After.
The purpose of Fragments After was to cover any loose ends or potential plot holes that were not touched on within the game itself. Fragments After also didn't get an English release until October 2019 (a solid 8 years after the initial release in December 2011).
The paradox that occurred for Alyssa to exist is also not explicitly shown in Final Fantasy XIII-2, but it occurs off-scene during the events of Final Fantasy XIII. As Serah and Nole begin fixing the timeline and paradoxes that occur in Final Fantasy XIII-2, they in-turn correct Alyssa's paradox as well.
During the events of Final Fantasy XIII, Alyssa became involved in the Purge when she visited her friend, Nena Stein, in Bodhum. She and Nena escaped and hid from the army with other Purgees, but they got buried under a pile of rubble in a cave-in. When the goddess Etro released the Pulse l'Cie who fought to defend Cocoon from crystal stasis, the resulting distortion of the timeline revived Alyssa. Since then, Alyssa has been having nightmares of her original fate and knows deep down she is living a lie.
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Final Fantasy XIII-2 Fragments After reveals that after betraying Serah and Noel, Alyssa accompanies Hope to the Augusta Tower in the guise of aiding in his investigation of an intruder in the system; in actuality, Alyssa is setting up a trap for Hope with the duplicates. After disposing the attacking duplicates, Hope finds a digital diary belonging to Alyssa that reveals her hate-filled thoughts towards the Pulse l'Cie, her fears of being erased with another taking her place, and her plotting to kill Hope. When she holds Hope at gunpoint Alyssa begins to disappear as Serah and Noel have fixed the paradox that allowed her to survive the cave-in. Alyssa begs Hope not to forget her before she ceases to be.
Nearly everyone's memories of Alyssa are erased with only Hope and a few people in Academy headquarters having vague memories of her. In Fragments After, it is revealed that a century later at 500 AF, Alyssa has been replaced by an intern named Aina Stein, an implied descendant of her friend Nena.