Due to an accident during the launch sequence, she and a group of other engineers got stranded on the ship. They spent the next millions of years waiting for a rescue.
Vasi was among the engineers who worked on Destiny in it's space dock on the Earth's orbit. While running final checks before ship's launch one of her team members detected a glitch in the system that could potentially jeopardize the mission.
While they wanted to fix it, the automated launch procedures were activated and the ship left the space dock, accelerating quickly away from Earth. With the ship going to fast to be intercepted and also being too close to Earth to dial the gate, Vasi and her team were advised to go into stasis and wait till the ship is far enough for a gate connection. With no other choice, the engineers went into stasis to wait for rescue. (SGU: "Back to Destiny 2")
After awakening from stasis and questioning Colonel Young on how his people got onboard, one of Vasi's teammates Irnas falls ill. Vasi makes Eli and Young help her get her people to a medical bay, which they protect with a shield, and soon after more of her people begin to get sick. Vasi sends Jota with Eli to get Lt. Johansen from stasis to see if she can help them. (SGU: "Back to Destiny 2")
Later, when the Destiny crew launches an attack on the Medical bay, Vasi collapses. When Dr. Gary Guzzo inspects her and her team, it's revealed Vasi and the Lanteans are sick with a cold or flu brought onboard by either the Tau'ri or the Lucian Alliance. Since Vasi and her team where in stasis for so long, their immune systems aren't prepared for the millions of years of bacterial evolution.
Later, Young informs Vasi of the Berzerker drones that have been blocking every Stargate in the galaxy and asks for her help and Camile Wray questions how much cooperation she's willing to give. Vasi responds that she and her team don't exactly have a home to go to now, so if they want to survive they should help each other. (SGU: "Back to Destiny 4")