They go back in time to when their sun was young and hydrogen rich and encase the entire star in a oversize <a href="http://en.wikipedia.org/wiki/General_Products">General Products Hull</a> that neatly encases their sun. Or perhaps, they are just good planners and don't need to travel back in time.

Due to the GP hull, the sun lasts longer than it otherwise would since it is not wasting its hydrogen on solar flares and solar wind. In the late stages, the additional pressure on the star keeps the star from even going into the giant/supergiant phase as the helium burning phase kicks in. During the main sequence phase, the fuel losses are actually quite minor, but they because quite large in the later stages of a star.

If the stellar radiation becomes too intense over time, your can even activate the Slaver stasis shield, turning on and off the sun rapidly, adjusting the duty cycle to match the desired level of radiation. This would also obviously extend the stars life.

This should extend the useful life of their sun by many millions, if not billions of year. If they are emotionally similar to the Puppeteers, they would perhaps prefer this method over evacuation anyway. It is similar to the Puppeteers solution to their problem in that respect.

I've read the *Fleet of Worlds* and know how the Puppeteers build a hull, so this is not completely practical at that level, but perhaps an alternate hull construction technique would be possible, or just another similar technology.

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Sadly, the real answer for the question as postulated is that it cannot be done. 10 years in not enough time to make any difference sans time travel. Even if you have fully advanced Von-Neuman machines at your service, you can't make a change to the core of your sun in ten years. No non-magical machine can penetrate to to core of a star and alter its composition. To prevent a nova, you have to change the core.  And if you have magic tech, surely you could evacuate to safety,