Postgres 10

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create table "table" (
 id int, 
 account int, 
 extra_account varchar(5),
 state varchar(10) default 'WORKS', 
 special_value int
)
insert into "table" (id, account, extra_account, special_value) values
  (100,111,'111-1',1)
, (200,111,'111-2',1)
, (300,222,'222-1',2)
, (400,333,'333-1',3)
, (500,333,'333-2',4)
5 rows affected

SELECT 
 STRING_AGG(DISTINCT extra_account, ', ' ORDER BY extra_account) AS extra_accounts
FROM (
  SELECT account, extra_account, special_value
  , ROW_NUMBER() OVER (PARTITION BY account, special_value ORDER BY id) AS rownum
  FROM "table" t
  WHERE account IN (111, 222, 333) 
    AND state = 'WORKS' 
) q
WHERE rownum = 1;


extra_accounts


111-1, 222-1, 333-1, 333-2