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.