Catalysis of the reaction: a pectate = a pectate + 4-(4-deoxy-alpha-D-galact-4-enuronosyl)-D-galacturonate. This reaction is the eliminative cleavage of 4-(4-deoxy-alpha-D-galact-4-enuronosyl)-D-galacturonate from the reducing end of pectate, i.e. de-esterified pectin.