No, a UNIQUE constraint can't be "conditional".
One option is to set the username column to NULL. The UNIQUE constraint will allow multiple rows with NULL value.
You could translate that to any string you wanted for display. either in the application, or in the SQL
SELECT IFNULL(t.username,'USER DELETED') AS username
FROM mytable t
If you are retaining these rows for historical/archive purposes, you probably do NOT want to update the username column. (If you change the value of the username column, then a subsequent statement will be allowed to insert a row with the same value as the previous username.)
You could instead add an additional column to your table, to represent the "user deleted" condition. For example:
user_deleted TINYINT(1) UNSIGNED DEFAULT 0 COMMENT 'boolean'
You could check this column and return the 'USER DELETED' constant in place of the username column whenever the user_deleted boolean is set:
SELECT IF(u.user_deleted,'USER DELETED',u.username) AS username
(Use a value of 1 to indicated a logical "user deleted" condition.)
The big advantage to this approach is that the username column does NOT have to be modified, the username value, and the UNIQUE constraint will prevent a new row with a duplicate username from being inserted.