I only meant to point out that you might have overlooked the user's functinality request. I was just giving my observation, often we do not know why in the world users want it. Nevertheless, I was trying the solution myself and tried couple of options,

1. First option was,

  1  create or replace trigger t_tgr after delete
  2  on t for each row
  3  declare
  4   pragma autonomous_transaction;
  5  begin
  6   update t set owner_id = id where owner_id is null;
  7   commit;
  8* end;
SQL> /

Trigger created.

 real: 100
SQL> select * from t;

        ID   OWNER_ID NAME
---------- ---------- ----------
         1          1 Cat
         2          1 Dog
         3          3 Mouse

 real: 60
SQL> delete from t where id = 1;
delete from t where id = 1
            *
ERROR at line 1:
ORA-00060: deadlock detected while waiting for resource
ORA-06512: at "APPS.T_TGR", line 4
ORA-04088: error during execution of trigger 'APPS.T_TGR'

2. Second was the statement level trigger that you have just shown. By the time I came back, you are already there with the solution.

SQL> create or replace trigger t_tgr after delete on t
  2  begin
  3   update t set owner_id = id where owner_id is null;
  4  end;
  5  /

Trigger created.

 real: 121
SQL> select * from t;

        ID   OWNER_ID NAME
---------- ---------- ----------
         1          1 Cat
         2          1 Dog
         3          3 Mouse

 real: 70
SQL> delete from t where id = 1;

1 row deleted.

 real: 30
SQL> select * from t;

        ID   OWNER_ID NAME
---------- ---------- ----------
         2          2 Dog
         3          3 Mouse


I DO AGREE THAT YOUR ORIGINAL SOLUTION TAKES IT IN THE RIGHT DIRECTION.
 

Tom,

I am totally confused now.  I ran the following script in Session A.

SQL> DROP TABLE t;

Table dropped.

Elapsed: 00:00:00.02
SQL>
SQL> CREATE TABLE t(ID INT PRIMARY KEY, owner_id REFERENCES t ON DELETE SET NULL, NAME VARCHAR2(100));

Table created.

Elapsed: 00:00:00.01
SQL>
SQL> INSERT INTO t VALUES (1, 1, 'Cat');

1 row created.

Elapsed: 00:00:00.00
SQL> INSERT INTO t VALUES (2, 1, 'Dog');

1 row created.

Elapsed: 00:00:00.00
SQL> INSERT INTO t VALUES (3, 2, 'Mouse');

1 row created.

Elapsed: 00:00:00.00
SQL>
SQL> COMMIT ;

Commit complete.

Elapsed: 00:00:00.00
SQL> SELECT * FROM t;

        ID   OWNER_ID NAME
---------- ---------- ----------------------------------------------------------------------------------
         1          1 Cat
         2          1 Dog
         3          2 Mouse

Elapsed: 00:00:00.00
SQL>
SQL> CREATE OR REPLACE TRIGGER t_trigger
  2     AFTER DELETE
  3     ON t
  4     FOR EACH ROW
  5  DECLARE
  6     PRAGMA AUTONOMOUS_TRANSACTION;
  7  BEGIN
  8     DBMS_OUTPUT.put_line ('Before');
  9
 10     UPDATE t
 11        SET owner_id = ID
 12      WHERE owner_id IS NULL;
 13
 14     DBMS_OUTPUT.put_line ('After');
 15     COMMIT;
 16  END;
 17  /

Trigger created.

Elapsed: 00:00:00.01
SQL>
SQL> delete from t where id = 1;
Before
After

1 row deleted.

Elapsed: 00:00:00.00
SQL>
SQL> select * from t;

        ID   OWNER_ID NAME
---------- ---------- ----------------------------------------------------------------------------------
         2            Dog
         3          2 Mouse

Elapsed: 00:00:00.00
SQL>

And I ran the same select statement in Session B and Output is 

SQL> select * from t;

        ID   OWNER_ID NAME
---------- ---------- ----------------------------------------------------------------------------------------------------
         1          1 Cat
         2          1 Dog
         3          2 Mouse

Could you please help in finding answers to these questions?

1.  As you said in yor previous posts, Its not creating deadlock.  What I am doing wrong?

2.  In the second session (Session B), I am expecting the output like this.....

SQL> select * from t;

        ID   OWNER_ID NAME
---------- ---------- ----------------------------------------------------------------------------------------------------
         1          1 Cat
         2          2 Dog
         3          2 Mouse

Why? Because the trigger in Session A, commited only 2nd record.  

3.  In the first session, Session A, I should get output like...

SQL> select * from t;

        ID   OWNER_ID NAME
---------- ---------- --------
         2          2 Dog
         3          2 Mouse

Why? Because already trigger updated second record.  (Even though it is automonous, Its in the same session).

Thanks for your time Tom.

Sincerely
Vaishnavi