Actually, converting to fiberglass is usually lighter than stock sheet metal(depending on how thick the glass was). Typically when this is done, a tubular roll cage is built to support the body, as well as provide the structural integrity of the vehicle. Unit-body refers to a type of construction where a vehicle's outer body and inner structure combine to create the strength to support the vehicle(Source of definition:
http://http://trucks.about.com/od/tr.../unit_body.htm). In the old days trucks were considered unibody since the bed and cab were connected, but the frame was separate. Nowadays, cars considered unibody still have large areas that are completely removable, such as the front clips.
So yes, to answer your question, you can have a safe, completely fiberglass body as long as its supported in some form.
EDIT>> Forgot to mention, unibody autos can be rebodied. Usually the "Body" is cut away from the pan, leaving the pan intact to be used as a base to work from.