SQL> CREATE OR REPLACE
   2     PROCEDURE DEAD_SYNONYM
   3       AUTHID CURRENT_USER
   4       IS
   5           v_Stmt VARCHAR2( 1000 );
   6           v_Cnt  NUMBER;
   7       BEGIN
   8           FOR v_Rec IN (
   9                         SELECT  *
  10                           FROM  USER_SYNONYMS
  11                        ) LOOP
  12             v_Stmt := 'SELECT COUNT(*) FROM DBA_OBJECTS';
  13             IF v_Rec.DB_LINK IS NOT NULL
  14               THEN
  15                 v_Stmt := v_Stmt || '@' || v_Rec.DB_LINK;
  16             END IF;
  17             v_Stmt := v_Stmt || ' WHERE OWNER = ''' || v_Rec.TABLE_OWNER ||
  18                         ''' AND OBJECT_NAME = ''' || v_Rec.TABLE_NAME || '''';
  19             EXECUTE IMMEDIATE v_Stmt INTO v_Cnt;
  20             IF v_Cnt =  0 
  21               THEN
  22                 IF v_Rec.DB_LINK IS NOT NULL
  23                   THEN
  24                     DBMS_OUTPUT.PUT_LINE('Synonym ' || USER || '.' ||
  25                                            v_Rec.SYNONYM_NAME ||
  26                                            ' points to nonexistent object ' ||
  27                                            v_Rec.TABLE_OWNER || '.' || v_Rec.TABLE_NAME ||
  28                                            '@' || v_Rec.DB_LINK);
  29                   ELSE
  30                     DBMS_OUTPUT.PUT_LINE('Synonym ' || USER || '.' ||
  31                                            v_Rec.SYNONYM_NAME ||
  32                                            ' points to nonexistent object ' ||
  33                                            v_Rec.TABLE_OWNER || '.' || v_Rec.TABLE_NAME);
  34                 END IF;
  35             END IF;
  36           END LOOP;
  37   END DEAD_SYNONYM;
  38   /

Procedure created.

SQL> create public synonym dead_synonym for dead_synonym;

Synonym created.

SQL> grant execute on dead_synonym to public;

Grant succeeded.

SQL> connect scott
Enter password: *****
Connected.
SQL> create table xxx(x number);

Table created.

SQL> create synonym xxx_syn for xxx;

Synonym created.

SQL> drop table xxx;

Table dropped.

SQL> set serveroutput on
SQL> exec dead_synonym
Synonym SCOTT.XXX_SYN points to nonexistent object SCOTT.XXX

PL/SQL procedure successfully completed.