CREATE TABLE `table_1` (
  `ID` int(10) unsigned NOT NULL auto_increment,
  `value` char(10) default NULL,
  PRIMARY KEY  (`ID`)
) ENGINE=InnoDB DEFAULT CHARSET=latin1;

CREATE TABLE `table_2` (
  `ID` int(10) unsigned NOT NULL auto_increment,
  `ID_table_1` int(10) unsigned default NULL,
  `value` char(10) default NULL,
  PRIMARY KEY  (`ID`),
  KEY `ID_table_1` (`ID_table_1`),
  CONSTRAINT `table_2_ibfk_1` FOREIGN KEY (`ID_table_1`) REFERENCES `table_1` (`ID`) ON DELETE CASCADE
) ENGINE=InnoDB DEFAULT CHARSET=latin1;

INSERT INTO table_1 (value) VALUES ('a'),('b'),('c'),('d');

INSERT INTO table_2 (ID_table_1, value) VALUES (2,'ha'),(2,'hb'),(NULL,'hc'),(NULL,'hd'), (1,'he'), (3,'hf');

mysql> select * from table_2;
+----+------------+-------+
| ID | ID_table_1 | value |
+----+------------+-------+
|  1 |          2 | ha    |
|  2 |          2 | hb    |
|  3 |       NULL | hc    |
|  4 |       NULL | hd    |
|  5 |          1 | he    |
|  6 |          3 | hf    |
+----+------------+-------+

ALTER TABLE table_2 CHANGE ID_table_1 ID_table_1 INT(10) UNSIGNED NOT NULL;

SHOW WARNINGS;
+---------+------+-------------------------------------------------+
| Level   | Code | Message                                         |
+---------+------+-------------------------------------------------+
| Warning | 1265 | Data truncated for column 'ID_table_1' at row 3 |
| Warning | 1265 | Data truncated for column 'ID_table_1' at row 4 |
+---------+------+-------------------------------------------------+


mysql> select * from table_2;
+----+------------+-------+
| ID | ID_table_1 | value |
+----+------------+-------+
|  1 |          2 | ha    |
|  2 |          2 | hb    |
|  3 |          0 | hc    |
|  4 |          0 | hd    |
|  5 |          1 | he    |
|  6 |          3 | hf    |
+----+------------+-------+

mysql> UPDATE table_2 SET ID_table_1=0 WHERE ID=3;
Query OK, 0 rows affected (0.00 sec)
Rows matched: 1  Changed: 0  Warnings: 0

mysql> UPDATE table_2 SET ID_table_1=5 WHERE ID=3;
ERROR 1216 (23000): Cannot add or update a child row: a foreign key constraint fails

mysql> UPDATE table_2 SET ID_table_1=0 WHERE ID=1;
ERROR 1216 (23000): Cannot add or update a child row: a foreign key constraint fails