Jesse, The module will not stop fluid to rear brakes, a bad master cylinder will,leaking lines, air in brake system, faulty metering block if equipped, collapsed flex lines or pinched brake line faulty caliper or brake cylinders,etc. will cause the possible feeling of no rear brakes.
(ABS Module components) the ABS speed sensors and the ABS control module . When the brake is applied, the ABS control module
reads the speed data from the speed sensor and sends the correct pressure to each wheel to prevent any wheel lock up, eg. sliding/skidding Links below have more info.
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Service Stability System AND abs Pump issue
ABS Control Module Replacement Service Cost YourMechanic