My coach is parked in my driveway and hooked up to shore power, so my batteries stay charged. For that reason I keep my dash camera on all of the time. It MAY record someone wandering in front of my coach before they do anything else.
I know that my Son uses digital battery powered game cameras to stake out deer hunting locations. The batteries seem to last several months and they do make cameras that will work at night and not spook the deer. A game camera MAY help to identify the next criminal.