Register of bruce is incorrectly written and it should be written as "fall of face to face" being its meaning: Found in front or unexpectedly with something or someone, stumble or fall upside down, snout unexpectedly.
be of bruce is incorrectly written and it should be written as "register of bruces" being its meaning: See: face to face.
The correct term is to go from face to face, although it is also given of face to face. It means falling off front and upside down.