Edit: or do you mean friendly nebula ships? They can't take out the AI command station, iirc, which means once they're gone (and they'll eventually make it back to your territory, or should) the alert goes away.
I mean the friendly ones that I cannot control. They just camp out in the center of the first planet they attack, unless there is a friendly planet adjacent to it.
Also, if you get a powerful champion I'm not sure the game can quite gg you from HW alert; you can probably take down whatever it does build up.
When I can't attack the HW guard posts, and everytime I attack, the AI sends a wave and initiates a cpa, it can easily be a gg, even with my ludicrously powerful champion fleet.
This is all hypothetical, but I think it should be dealt with (in fact, for a while, the escaped ships did not cause alert).
Edit: the Dawn class alone does not cause this.
Save attached, look at False Dilemma and Boolean (find them with the allied ships filter).
The save also has hacking-spawned zombies roaming the galaxy instead of attacking me. Is this intentional?