SQL> CREATE OR REPLACE TRIGGER tr_vr_dog_aiu
  2  AFTER INSERT OR UPDATE OF data_okon  ON vr_dog
  3  FOR EACH ROW
  4  begin
  5   update vr_rab set status_rab=decode(:new.data_okon,null,'Работает','Уволен') where id_rab=:new.id_rab;
  6  end;
  7  /

Trigger created.

SQL> select * from vr_dog;

    ID_RAB FIO                  DATA_OKO
---------- -------------------- --------
         1 Vlrznv               02.10.17
         2 Stax

SQL> ed
Wrote file afiedt.buf

  1* update vr_dog set data_okon=decode(data_okon,null,sysdate,null)
SQL> /

2 rows updated.

SQL> select * from vr_rab;

    ID_RAB STATUS_RAB
---------- --------------------
         1 Работает
         2 Уволен

SQL> select * from vr_dog;

    ID_RAB FIO                  DATA_OKO
---------- -------------------- --------
         1 Vlrznv
         2 Stax                 02.10.17

SQL>

при изменении в табличке VR_DOG в столбце DATA_OKON