DROP FUNCTION IF EXISTS GetLeaf;

DELIMITER @@;

CREATE FUNCTION GetLeaf(IN Root INT)
RETURNS INT
AS 
DECLARE PreviousNode INT;
DECLARE NextNode INT DEFAULT 0;
SET PreviousNode = Root;
BEGIN
    WHILE NextNode IS NOT NULL
        SELECT `Преемник` INTO NextNode
        FROM `table`
        WHERE `Контрагент` = PreviousNode
        LIMIT 1;
    END WHILE;
    RETURN PreviousNode;
END;
@@;

DELIMITER ;

SELECT GetLeaf(1) FROM DUAL;