Comment mettre à jour sur cascade dans MySQL?

Voici une solution qui utilise des clés étrangères en cascade pour faire ce que vous décrivez :

mysql> create table city (
  id int not null auto_increment, 
  name varchar(45), 
  active tinyint, 
  primary key (id),
  unique key (id, active));

mysql> create table person (
  id int not null auto_increment, 
  city_id int,
  active tinyint, 
  primary key (id), 
  foreign key (city_id, active) references city (id, active) on update cascade);

mysql> insert into city (name, active) values ('New York', 1);

mysql> insert into person (city_id, active) values (1, 1);

mysql> select * from person;
+----+---------+--------+
| id | city_id | active |
+----+---------+--------+
|  1 |       1 |      1 |
+----+---------+--------+

mysql> update city set active = 0 where id = 1;

mysql> select * from person;
+----+---------+--------+
| id | city_id | active |
+----+---------+--------+
|  1 |       1 |      0 |
+----+---------+--------+

Testé sur MySQL 5.5.31.