Who is at fault if a car backs into someone who is tailgating them?

Generally if you back into something it would be the backer's fault, unless both are backing and that will usually be that each would be responsible for their own vehicle damage. You shouldn't intentionally put it into reverse and back into someone that is following to closely. If you are stopped or moving slowly or have to stop sudddenly and they hit you in the rear the tailgater is at fault for following to close.