Oh yes, some people are lucky enough to live there ... and it will be their pleasure to show you around : the old "tuffeau" galleries (where the Loire castles stones were quarried), the 17th century silkworm farm (learn all about silk production in the region and the rearing of silkworms) and the traditional cave dwellings (hear about everyday life inside the rock).
Access to the site is by guided tour only. The 75min long visit is fun, educational and guided by one of the inhabitants. So, if you wonder why and how people still live "in there" nowadays : feel free to ask. Your host will be more than happy to explain and to invite you in.