How to create a conditional index in MySQL?
MySQL currently doesn't support conditional indexes.



To achive what you are asking (not that you should do it ;) ) you can start creating an auxiliary table:

CREATE TABLE  `my_schema`.`auxiliary_table` (
   `id` int unsigned NOT NULL,
   `name` varchar(250), /* specify the same way as in your main table */
   PRIMARY KEY (`id`),
   KEY `name` (`name`)
);


Then you add three triggers in the main table:

delimiter //

CREATE TRIGGER example_insert AFTER INSERT ON main_table
FOR EACH ROW
BEGIN
   IF NEW.status = 'ACTIVE' THEN
      REPLACE auxiliary_table SET
         auxiliary_table.id = NEW.id,
         auxiliary_table.name = NEW.name;
   END IF;
END;//

CREATE TRIGGER example_update AFTER UPDATE ON main_table
FOR EACH ROW
BEGIN
   IF NEW.status = 'ACTIVE' THEN
      REPLACE auxiliary_table SET
         auxiliary_table.id = NEW.id,
         auxiliary_table.name = NEW.name;
   ELSE
      DELETE FROM auxiliary_table WHERE auxiliary_table.id = OLD.id;
   END IF;
END;//

CREATE TRIGGER example_delete AFTER DELETE ON main_table
FOR EACH ROW
BEGIN
   DELETE FROM auxiliary_table WHERE auxiliary_table.id = OLD.id;
END;//

delimiter ;



  We need delimiter // because we want to use ; inside the triggers.


That way, the auxiliary table will contain exactly the IDs corresponding to the main table rows that contain the string "ACTIVE", being updated by the triggers.

To use that on a select, you can use the usual join:

SELECT main_table.* FROM auxiliary_table LEFT JOIN main_table
   ON auxiliary_table.id = main_table.id
   ORDER BY auxiliary_table.name;


If the main table already contains data, or in case you make some external operation that changes data in an unusual way (E.G.: outside MySQL), you can fix the auxiliary table with this:

INSERT INTO auxiliary_table SET
   id = main_table.id,
   name = main_table.name,
   WHERE main_table.status="ACTIVE";


About the performance, probably you'll have slower inserts, updates and deletes. This can make some sense only if you really deal with few cases where the condition desired is positive. Even that way, probably only testing you can see if the space saved really justifies this aproach (and if you are really saving any space at all).