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Xenosaga Episode 3 End Game Spoilers warning!
Wilhelm, taking the guise of Vector's CEO, is actually the guardian of the Lower Domain(reality) of the universe. He was created by the Collective Unconsciousness of the universe to protect the Lower Domain because if humanity ever(whether intentionally or accidentally) causes the destruction of the Lower Domain, the Higher Domain(realm of 'God') would fall as well.
After living at least over 6000 as an immortal protector Wilhelm discovered that humanity will eventually lead the universe to destruction through their actions over the millenniums. In order to stop this from happening, he devised a plan to use an ancient relic called Zarathustra to essentially reset the universe back to a previous time so that the universe will in essence live forever, thereby preventing its inevitable destruction. This process he called the Eternal Recurrence.
Shion's group eventually learns of his plan in the final chapter of the game and attempt to stop him, claiming that they can ensure the safety of the universe themselves without having to start over. Wilhelm is temporarily halted by one of his underlings(the testament Kevin) while Shion attempts to destroy Zarathustra once and for all. After destroying Zarathustra and foiling Wilhelm's plan, he seems relieved upon vanishing from sight. Even after seemly vanishing, he continues to exist proven by him assisting Shion's group in getting back to the Milky Way after they are nearly caught in a dimensional rift caused by the destruction of Zarathustra. While a villain in the game, his intention was always to save the universe.