Welcome to Eternity

I just listened to a blurb on NPR in which this guy thinks it's not out of the question that scientists are able to not only drastically slow the aging process, but......possibly even halt it?? That's kind of spooky. What happens when no one is dying, and yet everyone is still screwing (or at least procreating)? Or how about when our Sun starts to die, and cool, and shrink, to then only expand and overtake Earth's orbit? What then, Mr. Smarty?