I thought the issue with a light car was F=ma. The lighter your vehicle is the more likely you'll be used as a ping pong ball in any particular collision.
Well, not entirely...
In a big, "old", rigid steel cars (of yore...), the energy of the force of a collision was transferred to anything the could convert that energy...often it was passengers and other cargo that started moving around in the cabin, as kinetic energy...this would result is serious injury.
As technology (and manufacture...and regulation) improved, vehicles were made with "crumple-zones"...non cirtical (from a cabin perspective) portions of the vehicle that were intended to deform during a collision, converting the energy of a collision into potential energy (stored in the deformed, or "crumpled" portion of the vehicle). Along with that were added portions to reinforce the cabin, as well as improved restraint systems, to protect the occupants from being injured by parts of the vehicle itself, improving survival and reducing the chance of severe injury in a collision. These same principles can be applied regardless of the overall mass of the vehicle.
Of course, accident avoidance provides the best chance of not sustaining any injuries...