As the second star expands, becoming a Red Giant, its outer atmosphere might become caught up and pulled into orbit around the White Dwarf!

The Surface of the White Dwarf is VERY HOT and the gravitational pull VERY HIGH. The material from the Red Giant is rich in Hydrogen. If it falls to the surface of the White Dwarf, it will immediately set off a Thermo Nuclear Reaction.

If a little bit of mass falls onto the White Dwarf, we see a NOVA .

Many binary systems show re-occurring NOVA explosions.

However, if a LOT of mass falls on, or if the White Dwarf has been taking on more and more material, slowly, going off as a Nova again and again, it might SURPASS the Chandrasekhar Limit.

In this case, the ENTIRE WHITE DWARF WILL DISINTEGRATE as a SUPERNOVA!