Can a search-condition in CASE expression contain a subselect?

Is there a way to get around the restriction that the search-condition in CASE expression cannot contain a subselect?

Here are two queries I have tried and failed:

1) select userid,
     case
       when exists(select * from bank
           where bankid = user.custid)
         then 'bank'
       else 'non-bank'
     end case
   from user
2) select userid,
     case
       when custid in (select bankid
              from bank)
         then 'bank'
       else 'non-bank'
     end case
   from user

SELECT DISTINCT userid, 'bank'
FROM   user, bank
WHERE  user.custid = bank.bankid
UNION ALL
SELECT DISTINCT userid, 'non-bank'
FROM   USER, BANK
WHERE  NOT EXISTS (SELECT 1 FROM bank WHERE user.custid = bank.bankid);

SELECT user.userid, bank.bankid
FROM   user LEFT OUTER JOIN bank
ON     user.custid = bank.bankid;