Eight months into their journey, they found a Borgcube, and the Raven was pulled into that ship's transwarp conduit into the Delta Quadrant. The Raven continued to study of the Borg until 2356, when an ion storm damaged the vessel's shields, and they were detected by the Borg. The Hansens were assimilated, and the Raven crashed on a moon in B'omar space in the Agrat-Mot Nebula.(STreference: Star Charts)
Curiously, "A Ribbon for Rosie" states the Hansens' ship did not have a name, but only the numerical designation 32450 -- which was established at the same time as the name of the ship, in "The Raven".