The two planets, KOI 55.01 and KOI 55.02 actually had a significant effect on the evolution of their star, KIC 05807616. When observing the star, scientists noticed a variation in brightness... this, they discovered was due to light being emitted from the planets! Eliza Kempton from The University of California says:
"Light that is directly emitted or reflected from extrasolar planets has been detected in the past, but this is the first time that this particular method has been used for the discovery of a planetary system."
The reason for the survival of these planets is that they were large enough to strip the star of a significant amount of its mass. It is predicted that before the star became a Red Giant, the planets would have been large and gaseous, like Jupiter. As the star became a Red Giant, the planets were caught in its gravitational pull, and as they came closer, they stripped the star of some of its mass, while the star stripped them of their gaseous atmosphere, leaving only the solid core behind.
The difference between these planets and Earth is that these planets were much larger and closer to the star. When the sun turns into a Red Giant, all life on Earth will inevitably be destroyed, but it is possible that the planet itself will still survive.