An impossible planet?

The planet Halla may have once orbited two stars that interacted with one another by mass transfer as depicted. The eventual merger between the stars allowed Halla to escape engulfment and persist around the star that resulted from the merger. W. M. Keck Observatory/Adam Makarenko - When stars, similar to the sun, have reached the end of their lifetime, they inflate into red giant stars. The sun, for example, would then have a diameter hundreds of times larger than today. Whether the Earth will survive this final stage of its home star is uncertain. The planet called Halla around a sun-like star near Polaris, however, was lucky.