We would not see it until (if) it hit us.
Observation cannot travel faster than the speed of light. No matter what it is you're using to observe: Photons (light and radiation), measuring gravity, heat, anything. No matter if the phenomenon's expansion were traveling at the speed of light, the changes to the universe being made as well as our ability to observe them are also traveling at the speed of light.
If the phenomenon were very far away, we would not be able to observe anything it was causing until its leading edge caught up to us. Then we would be destroyed at exactly the same time. This is because in your example it is expanding at exactly the same rate as the universal speed-of-light constraint allows us to receive any indication of its presence. Any evidence of, e.g. a far away star being destroyed would take X amount of time to reach us by its light no longer arriving. However, in that time the edge of the space-destroying phenomenon will also hit us, because it will also take exactly X amount of time to reach us, at the speed of light, from the point where the star was when it was destroyed. The distance is the same, the speed is the same. We would continue to receive light from that star in the meantime, as we already do. (The light from the stars you see in the sky now is already tens/hundreds/thousands/millions/etc. years old depending on the distance to the star in question.)
If the phenomenon were so far away that it is outside of our observable field of the universe, it will never reach us and we will never have any indication of its presence. That's what "observable universe" means. Anything can happen anywhere outside of the observable universe and it is objectively meaningless to us, because we will never ever be able to reach it, record it, have it influence us in any way. This is, however, predicated on the theory of the perpetually expanding universe being true (which it probably is).
If you want to actually see the stars in your sky winking out over the millennia, I suggest building your universal destruction bomb such that its shockwave travels at, say, half the speed of light or some other suitable fraction.