If you've ever explored the Orion's Arm universe, you're probably awash with a lot of ideas that could fit within Sins as far as galactic super-dangers are concerned: (www.orionsarm.com) Space is just filled with things that could force your civilization into extinction, and asteroid and comet impacts are not some of them, being only planetary-scale disasters. When you consider how large the Vasari race probably is, and how much larger it was before they fled, whatever put them on the run must have been truly terrible. It obviously wasn't just a local event, as it spread rapidly and aggressively, and threatened their entire species. It still follows them. This puts a few different horrible things the Vasari could be running from to mind.
Here are some:
There are uncontrollable ever-expanding self-repairing nanite swarms that consume entire star systems of resources and leave that section of space an empty death trap. If the swarm develops intelligence it may move into interstellar space and become a galactic threat. They are generally created by biologicals for various benign purposes, or sometimes for warfare. On occasion they have escaped control of their creators and the result is truly terrifying. Humanity almost met its end to one of these, late in the interplanetary age, and was only saved due to the intervention of a recently-transcended archailect: (http://www.orionsarm.com/xcms.php?r=oaeg-view-article&egart_uid=4ad4d58752948)
There are things like Autowars, which are used often in warfare: (http://www.orionsarm.com/xcms.php?r=oaeg-view-article&egart_uid=45eb1ea444972) Automated self-replicating super-intelligent warship factories that endlessly pump out highly-advanced warships into massive armadas designed to destroy whatever their creators designed them to. In some cases the autowar fleets have gone rogue, and like the runaway nanite swarms have managed to wreck extensive havoc before being subdued. A few times in galactic history they managed to destroy their creators: (http://www.orionsarm.com/eg-article/4b6d2e7446c5a)
The Dawn Hunters are an example of a supposed legendary autowar fleet that destroyed its creator civilization millions of years ago and still exists as a blight upon the galaxy, suspected of having wiped out numerous intelligent civilizations over the past several million years. According to the theory they are still lurking in the galaxy, somewhere near Terragen space: (http://www.orionsarm.com/xcms.php?r=oaeg-view-article&egart_uid=480135af5ac81)
The Hedrile: (http://www.orionsarm.com/eg-article/48013e3b67f3e) A strange alien artifact that is billions of years old, supposedly contains a wormhole that leads to another universe, and has led to the disappearance of several transcendent AIs that attempted to plumb its depths. Built by an ancient civilization which no longer exists, either because they went through it and could not come back, or because whatever they connected it to came through and destroyed them.
The Omicron Hygeras Object: (http://www.orionsarm.com/eg-article/4a59d19f81fed) A 262 kilometer long object that appears to be of extragalactic origin, and is approximately 400 million years old. Emits heavy radiation, and is surrounded by powerful magnetic and gravitational fields. It orbits a star that once was home to an interstellar race that subsequently vanished upon the object's arrival. It has defied all attempts at either being explored, occupied, or demolished, and has resulted in the deaths of thousands of would-be explorers, archaeologists, and even some transcendent AIs.
The Iahi Daon Empire: (http://www.orionsarm.com/eg-article/48fa48fb5a4ae) Ancient extinct civilization of which numerous dead ark ships have been discovered floating in interstellar space. Similar to the Vasari in that they hastily fled their homeworld and most occupied systems 7,233,000 years ago, fleeing something unknown. Unlike the Vasari the Iahi Daon did not escape their menace, and died out without being able to restore their empire.
There are a lot more possibilities I could list, all of them tantalizing and fittable within the Sins cosmology, since we know almost nothing about what the Threat could be. I hope it is something fantastic, but it will probable be something pretty mundane, like a nanite swarm.
I'll leave you with this, a picture of the Orion's Arm galaxy and the location of its various high-energy civilizations: (http://www.orionsarm.com/xcms.php?r=oaeg-view-article&egart_uid=48028a7f74e6d) Notice that the right half of the galaxy has almost no detectable energy emissions. Why is that section of the galaxy seemingly devoid of technologically advanced life while the rest of the galaxy is not? When I am playing Sins, I often imagine that the Vasari must hail from that part of the galaxy, and whatever is chasing them has consumed everything there. Some terrifying thing must have caused the right half of the Milky Way in the Orion's Arm universe to die millions of years ago. I wonder if it is the same thing that is chasing the Vasari? Did the Vasari build something like the Hedrile, and a cosmic terror came through? Did a weapon of utterly MASS destruction like the Omicron Hygeras Artifact arrive from another galaxy? Did the Vasari meet an impossibly powerful ancient menace left over from a previous civilization, like the Dawn Hunters? Did the Vasari create an autowar fleet they lost control of, or a was there a nanodisaster they never subdued?
It's fun speculating.