My Exodus Scenario (SE4 Classic) was based on just such an occurrence.
More importantly, though, the race was played as if it were a neutral for about 150 turns before the event...
When I played, I built a set of huge transports that grabbed at least half of the population plus some miscellaneous units, and a couple of colony ships.
I decided to go south. While there was only one breathable planet there, I had squandered too much time on preparations, and couldn't risk running out of resources partway through the invasion of the more distant, but bountiful northern systems.
My army of dreadnoughts pushed the 1st place Ukra-Tal out of one of the systems, but we had to glass a lot of worlds (40% loss in value).
Shortly after the system was swept, the star blew.
All but one dreadnought eventually had to be put in mothballs over the only breathable world, and my entire military shuffled between the colonies and interception missions as U-T baseships wandered by.
I filled up on mineral miners, but with only 3 planets at 50% value or so, it was a very thin budget.
I built up fighters, but between the lack of funds and the thick PD of the baseships, it was tough to keep the numbers up.
My Nature Shrine helped immensely, boosting the budget by 6% each decade, even though I couldn't afford to colonize and protect any more planets.
Eventually I was able to bring more of the ancient dreadnoughts Online again, like great mythical warriors from the depths of time.
I moved from running interceptions, to covering the three planets, to actually blockading the warppoints. Then I was able to fully expand to all of the colonizable worlds in the system, and finally see victory at hand!
[ December 09, 2003, 22:13: Message edited by: Suicide Junkie ]