[oracle] Is it possible to CONTINUE a loop from an exception?

How about the ole goto statement (i know, i know, but it works just fine here ;)

DECLARE
   v_attr char(88);
CURSOR  SELECT_USERS IS
SELECT id FROM USER_TABLE
WHERE USERTYPE = 'X';
BEGIN
    FOR user_rec IN SELECT_USERS LOOP    
        BEGIN
            SELECT attr INTO v_attr 
            FROM ATTRIBUTE_TABLE
            WHERE user_id = user_rec.id;            
         EXCEPTION
            WHEN NO_DATA_FOUND THEN
               -- user does not have attribute, continue loop to next record.
               goto end_loop;
         END;

        <<end_loop>>
        null;         
    END LOOP;
END;

Just put end_loop at very end of loop of course. The null can be substituted with a commit maybe or a counter increment maybe, up to you.