I would also like to point out that activating the halo rings does not grant an automatic win here. As the rings will also destroy all of the halo universe it is not a victory and the way I see it, it is an omission of defeat that you could not defeat star wars with out also destroying yourself.
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Halo characters hide in shield worlds, thus they win. Also, the forerunners prepared for the Halo rings being fired by making it so the galaxy can be repopulated, but star wars would have lost by then.
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The Flood would still be alive, not all of it would be wiped out.