Brake master stoppers stop the brake mnaster cylinder from moving and flexing in the firewall. Get a mate to pump the brake pedal hard while you look at the cylinder.... you'll see it move as the firewall flexes. This movement is stealing clamping pressure from the caliper pistons. I've seen quite a few J-spec cars come from Japan with brake master stoppers, but they never look like that. I've been after one for a while.
Some are just bolted into the strut tower area, but the real nice ones have an adjustable screw so you can really push on the cylinder and prevent any movement.