It appears that, in Oracle 11, the * and + patterns (with nothing preceding them) generate zero-width matches. So (*) and (+) are capturing groups () containing the zero-width patterns * or + respectively.
All these queries return a row:
SELECT * FROM DUAL WHERE REGEXP_LIKE( '1', '*' );
SELECT * FROM DUAL WHERE REGEXP_LIKE( '1', '(*)' );
SELECT * FROM DUAL WHERE REGEXP_LIKE( '1', '^*' );
SELECT * FROM DUAL WHERE REGEXP_LIKE( '1', '^(*)' );
SELECT * FROM DUAL WHERE REGEXP_LIKE( '1', '*1' );
SELECT * FROM DUAL WHERE REGEXP_LIKE( '1', '+' );
SELECT * FROM DUAL WHERE REGEXP_LIKE( '1', '(+)' );
SELECT * FROM DUAL WHERE REGEXP_LIKE( '1', '^+' );
SELECT * FROM DUAL WHERE REGEXP_LIKE( '1', '^(+)' );
SELECT * FROM DUAL WHERE REGEXP_LIKE( '1', '+1' );
SELECT * FROM DUAL WHERE REGEXP_LIKE( '1', '^+1' );
SELECT * FROM DUAL WHERE REGEXP_LIKE( '1', '+1$' );
SELECT * FROM DUAL WHERE REGEXP_LIKE( '1', '^+1$' );
SELECT * FROM DUAL WHERE REGEXP_LIKE( '1', '()' );
SELECT * FROM DUAL WHERE REGEXP_LIKE( '12', '1(*)2' );
SELECT * FROM DUAL WHERE REGEXP_LIKE( '12', '1(+)2' );
These queries do not return any rows:
SELECT * FROM DUAL WHERE REGEXP_LIKE( '1', '*2' );
SELECT * FROM DUAL WHERE REGEXP_LIKE( '1', '^*$' );
SELECT * FROM DUAL WHERE REGEXP_LIKE( '1', '^+$' );
SELECT * FROM DUAL WHERE REGEXP_LIKE( '12', '11(*)2' );
SELECT * FROM DUAL WHERE REGEXP_LIKE( '12', '11(+)2' );
Also, matching any pattern against NULL or a string against a NULL pattern will not return any rows:
SELECT * FROM DUAL WHERE REGEXP_LIKE( NULL, '*' );
SELECT * FROM DUAL WHERE REGEXP_LIKE( '1', NULL );
Using REGEXP_SUBSTR:
SELECT REGEXP_SUBSTR( '1', '+' ) FROM DUAL;
Outputs a single row containing NULL.