The stamped metal piece at the bottom of the assembly has to contact the adjuster that spreads the brake shoes to maintain close contact to the brake drum. There is a right and a left to these parts and they are marked with "L" and "R". When the car is reversed the metal piece drops down and picks up a tooth on the adjuster and pulls it upwards when the brake is released, if you have reversed the pieces, they won't engage. These parts do wear out and are commonly available new.
I like to put a small dab of anti-seize on the contact points on the backing plates (where the brake shoe metal touches) and on the threads of the adjuster. Old backing plates will have a groove worn in the metal from contact at 6 places, you can grind it smooth if it is a small groove or fill it with weld if it is deep and then grind smooth. Disc brakes are great on the front and drum brakes are better on the rear for parking brake, wedging effect, simplicity, etc. etc..