Postgres 13

By using db<>fiddle, you agree to license everything you submit by Creative Commons CC0.
CREATE TABLE tbl_ab(ab text PRIMARY KEY);

CREATE TABLE tbl (
  a text REFERENCES tbl_ab ON UPDATE CASCADE ON DELETE CASCADE
, b text REFERENCES tbl_ab ON UPDATE CASCADE ON DELETE CASCADE
);

-- trigger to take care of it in the background
CREATE OR REPLACE FUNCTION trg_tbl_insbef()
  RETURNS trigger AS
$func$
BEGIN
   INSERT INTO tbl_ab(ab)
   SELECT NEW.a WHERE NEW.a IS NOT NULL  -- NULL is allowed (?)
   UNION ALL
   SELECT NEW.b WHERE NEW.b IS NOT NULL;

   RETURN NEW;
END
$func$ LANGUAGE plpgsql;

CREATE TRIGGER tbl_insbef
BEFORE INSERT ON tbl
FOR EACH ROW EXECUTE PROCEDURE trg_tbl_insbef();
INSERT INTO tbl(a,b) VALUES ('x', 'y');
1 rows affected

-- NULL values are allowed
INSERT INTO tbl(a,b) VALUES (NULL, NULL);
1 rows affected

TABLE tbl;


a
b


x
y

null
null


TABLE tbl_ab;


ab


x

y


-- not allowed
INSERT INTO tbl(a,b) VALUES ('x', 'y');
ERROR:  duplicate key value violates unique constraint "tbl_ab_pkey"
DETAIL:  Key (ab)=(x) already exists.
CONTEXT:  SQL statement "INSERT INTO tbl_ab(ab)
   SELECT NEW.a WHERE NEW.a IS NOT NULL  -- NULL is allowed (?)
   UNION ALL
   SELECT NEW.b WHERE NEW.b IS NOT NULL"
PL/pgSQL function trg_tbl_insbef() line 3 at SQL statement


-- not allowed
INSERT INTO tbl(a,b) VALUES ('y', NULL)
ERROR:  duplicate key value violates unique constraint "tbl_ab_pkey"
DETAIL:  Key (ab)=(y) already exists.
CONTEXT:  SQL statement "INSERT INTO tbl_ab(ab)
   SELECT NEW.a WHERE NEW.a IS NOT NULL  -- NULL is allowed (?)
   UNION ALL
   SELECT NEW.b WHERE NEW.b IS NOT NULL"
PL/pgSQL function trg_tbl_insbef() line 3 at SQL statement


-- not allowed
INSERT INTO tbl(a,b) VALUES (NULL, 'x')
ERROR:  duplicate key value violates unique constraint "tbl_ab_pkey"
DETAIL:  Key (ab)=(x) already exists.
CONTEXT:  SQL statement "INSERT INTO tbl_ab(ab)
   SELECT NEW.a WHERE NEW.a IS NOT NULL  -- NULL is allowed (?)
   UNION ALL
   SELECT NEW.b WHERE NEW.b IS NOT NULL"
PL/pgSQL function trg_tbl_insbef() line 3 at SQL statement


-- not allowed
INSERT INTO tbl(a,b) VALUES ('z', 'z');
ERROR:  duplicate key value violates unique constraint "tbl_ab_pkey"
DETAIL:  Key (ab)=(z) already exists.
CONTEXT:  SQL statement "INSERT INTO tbl_ab(ab)
   SELECT NEW.a WHERE NEW.a IS NOT NULL  -- NULL is allowed (?)
   UNION ALL
   SELECT NEW.b WHERE NEW.b IS NOT NULL"
PL/pgSQL function trg_tbl_insbef() line 3 at SQL statement
a	b
x	y
null	null