I have read check documentation: https://checkstyle.org/checks/javadoc/javadocparagraph.html
I have downloaded the latest checkstyle from: https://checkstyle.org/cmdline.html#Download_and_Run
I have executed the cli and showed it below, as cli describes the problem better than 1,000 words

Detected at: #15503 (comment)

In JavadocParagraph's implementation, we're only checking for P tags which aren't closed, i.e we're checking only for <p> which doesn't have corresponding </p>.

There is a difference in parsed AST when P have its corresponding closing tag and when it doesn't have it. As explained in the above referenced comment, AST for P when it is not closed looks like this:

    |   |   |       |--HTML_ELEMENT -> HTML_ELEMENT [4:3]
    |   |   |       |   `--P_TAG_START -> P_TAG_START [4:3]

and when it is properly closed, it looks like this:

    |   |   |       |--HTML_ELEMENT -> HTML_ELEMENT [4:3]
    |   |   |       |   `--PARAGRAPH -> PARAGRAPH [4:3]
    |   |   |       |       |--P_TAG_START -> P_TAG_START [4:3]

A new PARAGRAPH appears between the token.

What we do in the Check's implementation:

We check if after HTML_ELEMENT is there a P_TAG_START token? This token is for opening paragraph tag ( <p> ). If yes then move further.

This case is only valid for <p> tags which does not have their corresponding </p>, so when we encounter a proper pair of paragraph tag (<p></p>), our check ignores that paragraph as a new token ( PARAGRAPH ) appears between HTML_ELEMENT & P_TAG_START.

Example:

$ cat .\javadocparagraph_config.xml
<?xml version="1.0"?>
<!DOCTYPE module PUBLIC
          "-//Checkstyle//DTD Checkstyle Configuration 1.3//EN"
          "https://checkstyle.org/dtds/configuration_1_3.dtd">

<module name="Checker">
  <module name="TreeWalker">
    <module name="JavadocParagraph"/>
  </module>
</module>

$ cat .\InvalidParagraphTagPosition.java
/**
 * Some summary.
 *
 * <p>  Some Javadoc.
 *
 * <p>  Some Javadoc. </p> // false-negative
 */
public class InvalidParagraphTagPosition {
    /**
     * some javadoc.
     * <p>
     *
     * <p></p> // false-negative
     */
    int a;

    /**
     * Some Javadoc.<P>
     * Some Javadoc.<P></P> // false-negative
     */
    int b;
}

$ java -jar .\checkstyle-10.18.1-all.jar -c .\javadocparagraph_config.xml .\InvalidParagraphTagPosition.java
Starting audit...
[ERROR] C:\checkstyle testing\.\InvalidParagraphTagPosition.java:4: <p> tag should be placed immediately before the first word, with no space after. [JavadocParagraph]
[ERROR] C:\checkstyle testing\.\InvalidParagraphTagPosition.java:11: <p> tag should be placed immediately before the first word, with no space after. [JavadocParagraph]
[ERROR] C:\checkstyle testing\.\InvalidParagraphTagPosition.java:11: <p> tag should be preceded with an empty line. [JavadocParagraph]
[ERROR] C:\checkstyle testing\.\InvalidParagraphTagPosition.java:18: <p> tag should be placed immediately before the first word, with no space after. [JavadocParagraph]
[ERROR] C:\checkstyle testing\.\InvalidParagraphTagPosition.java:18: <p> tag should be preceded with an empty line. [JavadocParagraph]
Audit done.
Checkstyle ends with 5 errors.

We get errors only for <p> which are not closed, we don't get any violations for <p> which are closed properly. We expect the same errors as we got for <p>

Describe what you expect in detail.

Fix the check's implementation to check for both types of tags: <p> & <p></p>