I got it. See elaborate code below:
Turns out it was simpler than expected.
-- Dumping database structure for test
CREATE DATABASE IF NOT EXISTS `test` /*!40100 DEFAULT CHARACTER SET latin1 */;
USE `test`;
-- Dumping structure for table test.table_a
CREATE TABLE IF NOT EXISTS `table_a` (
  `id` int(11) NOT NULL AUTO_INCREMENT,
  `name` varchar(50) DEFAULT NULL,
  `value` int(11) DEFAULT NULL,
  PRIMARY KEY (`id`)
) ENGINE=InnoDB AUTO_INCREMENT=2 DEFAULT CHARSET=latin1;
INSERT INTO `table_a` (`id`, `name`, `value`) VALUES
    (105, 'test1', 1000);
CREATE TABLE IF NOT EXISTS `table_b` (
  `id` int(11) NOT NULL AUTO_INCREMENT,
  `tbl_a_fk` int(11) DEFAULT NULL,
  `name` varchar(50) DEFAULT NULL,
  `value` int(11) DEFAULT NULL,
  PRIMARY KEY (`id`),
  KEY `FK_table_b_table_a` (`tbl_a_fk`),
  CONSTRAINT `FK_table_b_table_a` FOREIGN KEY (`tbl_a_fk`) REFERENCES `table_a` (`id`)
) ENGINE=InnoDB AUTO_INCREMENT=8 DEFAULT CHARSET=latin1;
INSERT INTO `table_b` (`id`, `tbl_a_fk`, `name`, `value`) VALUES
    (1, 105, 'test1', 400),
    (2, 105, 'test2', 400),
    (3, 105, 'test3', 50),
    (7, 105, 'test4', 100);
DELIMITER //
CREATE TRIGGER `table_b_before_insert` BEFORE INSERT ON `table_b` FOR EACH ROW BEGIN
    SET @_sum = (SELECT sum(value) from table_b where tbl_a_fk=new.tbl_a_fk);
    SET @_units = (SELECT value from table_a where id=new.tbl_a_fk);
    set @msg = "Value Surpassed";
    IF @_sum > @_units THEN
    SIGNAL SQLSTATE '45000' SET MESSAGE_TEXT = @msg;
    END IF;
END//
DELIMITER ;
insert into table_b values(null,105,'test5',100);