Just about the simplest solution I can think of is using wave forms. Flame from the sun or otherwise is the vibration of molecules.by generating a force wave capable of stopping this vibration essentially freezing the star in place could be all It would take.. Be it with lasers tractorbeams or a mechanical trap pulsating expansions and contractions targeted at alligning the mass into a stable non burning mass.
To add a little clarity as commenter did seem to have missed the key to the proposition,3d wave forms are a new science in function where scientists are using speakers to manipulate matter in a 3 dimetionaldimensional area. levitating small Every day objects with no more than sound waves. Upscaling this technology to calculate the estimated location of the particles composing the sun,a frequency targeted at moving the particles into a state where they would align and sit in a state of rest to stop the chain reaction of the sun's burn. More like using a pulse grenade to put out a house that was on fire. The burst would not equal the total mass force of the house but mearlymerely vibrate the air so as to flash off the flame.