Gracias a las anteriores soluciones llegue a esto:
USE JUGOS_VENTAS;
DROP PROCEDURE IF EXISTS LIMITE_CREDITOS;
DELIMITER $$
USE JUGOS_VENTAS$$
CREATE PROCEDURE LIMITE_CREDITOS()
BEGIN
DECLARE TMPCREDITO INT;
DECLARE FLAG BIT(1) DEFAULT 1;
DECLARE ACCUMULATE INT DEFAULT 0;
DECLARE LCURSOR CURSOR FOR SELECT LIMITE_dE_CREDITO FROM TABLA_DE_CLIENTES;
DECLARE CONTINUE HANDLER FOR NOT FOUND SET FLAG = 0;
OPEN LCURSOR;
WHILE FLAG = 1
DO
FETCH LCURSOR INTO TMPCREDITO; -- This gives NOT FOUND when reach the end
IF FLAG = 1 -- VERY IMPORTANT, BECAUSE IT CAN CAUSE SUM TWICE THE LAST COLUMN
THEN
SET ACCUMULATE = ACCUMULATE + TMPCREDITO;
END IF;
END WHILE;
CLOSE LCURSOR;
SELECT CONCAT("EL LIMITE TOTAL ES: ", ACCUMULATE);
END$$
CALL LIMITE_CREDITOS;
SELECT SUM(LIMITE_DE_CREDITO) FROM TABLA_DE_CLIENTES; -- to check the result
Espero les sirva.