It's important to note that the average density is low, it doesn't mean it's uniformly that dense. I cannot speak for this star in particular, but a lot of variable stars expand and contract so fast that material actually bounces off of it sending out a shell that may or may not re-coalesce or continue going off into space. The shell continues to glow due to the heat it already had, and the heat it receives from the main part of the star.