I do like the idea of applying it to all stars bassed on their age. And providing players with an ability to stabilise a star.
although im a bit wary about how realistic this is... Stars live for a REALLY REALLY long time, even if we assume that time is significantly faster in game than in RL then realistically youd still only expect one or two naturally occuring SuperNovas per year of game time. Perhapes you could do it in reverse, instead of SuperNovas happening naturally and players stopping it. Perhapes players could instigate a supernova, by destabilising a star that they dont like anymore. Having said that its also not too realistic that stars just sort of materialise out of thin air with a full system in tow. However who hasnt dreamed of blowing up a star
and heck this is a game, in the end game balance and hence fun for all is more important than sticking rigidly to reality. However perhapes some stars could go SuperNova all by themselves occasionally.
It could be achieved with either one module that can nudge a stars stability in either direction, or two moduels, one for stabilisng the other for destabilising. If a stars stability goes below a certain level then it goes critical and you have a limited time to evacuate before it goes super nova. I suggest being able to both stabilise and destabilise since otherwise it could be a pretty effective weapon.
The module could be researched/built to different levels to provide different speeds, but i think it should probably be capped in some way like the tactical advantage is.
I also think setting a minimum & maximum number of stars in a quadrant is a good idea as well. Random chance can bite you in the arse sometimes, without them it would be possible for a quad to have virtually no stars and another to have a whole bunch.
EDIT an interesting combination of resource left and player controlled SuperNova is to have the systems base health determined by the amount of resource in it. So as a system is mined out it becomes easier to destabilize. a system where only the top 10% of resource is used is difficult to destabilise one with 90% depleted is a lot easier. What you want to avoid is a player setting out to mine just the valuable resources and then quickly forcing a supernova so that a new system generates and repeating the process.