However, planets that were outside the original HZ may find themselves in the new HZ. Once frozen planets will warm up, and water will flow. For a few billion years, life will have a second chance. Life here on Earth took around 2.8 to 3.5 billion years or so to evolve to the point where we are today. If there was an advanced civilization on one of the inner planets, there is a rather good chance that they have at least sent probes to the outer planets, and contaminated them with microbial life (eukaryotic), giving life a kick start, shaving off billions of years of evolution (eukaryotic cell organisms developed 1.5 billion years ago - from the eukaryotic cells evolved multicellular life forms).
It's an interesting premise - what would life be like for a civilization rising up in the senior years of its star?
NASA/Goddard Space Flight Center. "New Frontier Opens In The Search For Life On Other Planets." ScienceDaily 18 April 2005. 4 November 2007