In 2267, the Botany Bay was discovered by the USS Enterprise, where Kati was one of thirty women among the 72 surviving members of Khan's original group of 84. She was exiled to Ceti Alpha V with the rest of Khan's people after a failed attempt to capture the Enterprise. (TOS: "Space Seed")
6 months later however Ceti Alpha XI exploded and laid waste to Ceti Alpha V, leaving only the transported cargo crates as shelter.
Whether she survived to serve Khan on the stolen USS Reliant 15 years later or was killed by the life forms of the planet is unknown. What ever the case, Kati would be deceased. Star Trek II: The Wrath of Khan