In the new reality that resulted from the Crisis on Infinite Earths, Power Girl was displaced from her native reality of Earth-Two. Becoming an anomaly on the post-Crisis merged Earth, Kara Zor-L for a time believed she was the granddaughter of the ancient Atlantean superhero known as Arion. When, in fact, this deception was revealed... she regained her interest in seeking out her home universe and the world on which she first carved out the legend that was her caped alter ego.
She was able to to locate Earth-Two once more after the machinations of Earth-Three's Alex Luthor and Earth-Prime's Superboy unleashed yet another Crisis upon the Multiverse. When she regained contact with her old allies, now members of the Justice Society of Infinity, she soon learned that she was a temporal clone spawned from the Crisis event, with the original version of Power Girl having roamed through that universe seeking out the location of their cousin Superman and his wife Lois, who had been in a pocket dimension with Luthor and Superboy for years.
Once determining that she had no place in this realm which had moved on without her, since the Society members Doctor Fate and Spectre had shielded off this reality from the rest of the Multiverse in order to preserve its integrity, she returned to the post-Crisis world that was now her home and accepted that this is where she was supposed to be.
Another lost voyager of the parallel realities was Red Tornado, and the being that merged with him in the Tornado Champion. At once point, it was his unique nature as a creature of twin universes that inspired the evil Creator2 to use this android as a bridge between realities, merging Earths One and Two together in order to clear a path for an intergalactic space-lane he was hired to procure by an alien race. Thankfully, the same Doctor Fate and Spectre were able to turn Creator2's technology against him, freeing the Red Tornado and saving both worlds. Perhaps this incident was the genesis of their idea to segment Earth-Two's dimensional plane from the other realities years later.