Why would the left rear wheel of a 1992 Chevy Cavalier lock up when you step on the brakes but not if in reverse?
You probably have the brake pads reversed. There is one for the front side and another for the rear. The shorter one should be in the front.
It's usually caused by a leak in your wheel cylinder. The part itself is around $10.00, but be careful when you remove the brake line, it is very easy to break. It could also be: the rear brakes were wrongly made by the manufacture and so were the specs dispersed to all other companies to it warps horribly the wheel cylinder master cylinder.
check your internal parts of the drum brake on the particular side of vehicle, they are usually set up with an automatic brake adjuster that works when putting vehicle in reverse and lightly applying brakes while moving in reverse which adjusts your drum brakes, this part may be worn out and need replaced , most parts stores carry a hardware kit for your replacement brakes for any vehicle