I don't have the Leviathan expansion for Stellaris, but the Spectre Wraith, is that the one that looks like a huge Alien sticking out of a black hole?
Because I know that you can end up with one of those if you follow the entire Horizon's Signal story chain (it starts by you sending scientists into an anomaly and end up losing them, "What is was, what was shall be"). It ended up in my home system (could be because that's where I completed a certain building, can't recall for certain). But this was already past the point in the game where I had crushed the Unbidden so sending in the fleets took care of it.
The quest chain does give you a very nice unique building, 2 even if you're willing to take a little happiness hit on a planet, they both have 'Loop' in their names. I wonder if it's possible to obtain them and subsequently axe the story thread so the monster won't spawn.