Tyranids eat man , elder , orks and Tau ( and anything else that's eatable )
Chaos dies ( nothing to sustain them )
Necrons sit and wait till the tyranids either starve ( or turn on themselves to sustain higher hive creatures ) or bugger off .
Necrons are now the rulers till the destroyers get bored and decide to anhialate the last living remanants ( ie , the other Necrons ) .
This is actually a really good analysis. The Tyranids in particular should be fundamentally unstoppable. The hive fleets are so large they are visible as interstellar structures
. It's difficult to really grasp that scale. The hive fleets could eat every single occupied planet in the galaxy and probably 0.00000001% of them would even realize they encountered resistance. Of course, plot armor prevents this, but ....
The necrons of course don't give a crap about living on worlds that have been stripped of life (heck, their pylons do this) so inheriting Tyranid discards would be just fine for them. Although I'm sure they'd be retroactively pissed that there was so much life they missed having a chance to kill. But they're used to being safely buried for billions of years, so whatevs.