Which methods can be used to return valid and invalid XML data from a file in Java?

Firstly, you're confusing valid and well-formed. You say you want to find invalid elements, but your examples aren't just invalid, they are ill-formed. That means that no XML parser is going to do anything with them other than throwing an error message at you. You can't use JAXB or XPath, or XQuery, or XSLT, or anything to process something that isn't XML.

You say "unfortunately I do not have access to the system that sends this xml format". I'm not sure why you call it an XML format: it isn't. I also don't understand why you (and many others on StackOverflow) are prepared to spend your time digging in garbage like this rather than telling the sender to get their act together. If you were served a salad with maggots in it, would you try to pick them out, or would you send it back for replacement? You should adopt a zero-tolerance approach to bad data; that's the only way senders will learn to improve the quality.

If the file contains lines with start and end tags who's name begins with "Product", you could:

• use a file scanner to split this document into individual pieces whenever a line starts with <Product or </Product
• attempt to parse the extracted text as XML using an XML API.
  • If it succeeds, add that object to a list of "good" well-formed XML documents
    • then perform any additional schema validation or validity checks
  • If it throws a parse error, catch it, and add that snippet of text to the list of "bad" items that need to be cleaned up or otherwise handled

An example to get you started:

package com.stackoverflow.questions.52012383;

import org.w3c.dom.Document;
import org.xml.sax.InputSource;
import org.xml.sax.SAXException;

import javax.xml.parsers.DocumentBuilder;
import javax.xml.parsers.DocumentBuilderFactory;
import javax.xml.parsers.ParserConfigurationException;

import java.io.File;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.StringReader;

import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class FileSplitter {

    public static void parseFile(File file, String elementName) 
      throws ParserConfigurationException, IOException {

        List<Document> good = new ArrayList<>();
        List<String> bad = new ArrayList<>();

        String start-tag = "<" + elementName;
        String end-tag = "</" + elementName;
        DocumentBuilderFactory factory = DocumentBuilderFactory.newInstance();
        DocumentBuilder builder;
        StringBuffer buffer = new StringBuffer();
        String line;
        boolean append = false;

        try (Scanner scanner = new Scanner(file)) {
            while (scanner.hasNextLine()) {
                line = scanner.nextLine();

                if (line.startsWith(startTag)) {
                    append = true; //start accumulating content
                } else if (line.startsWith(endTag)) {
                    append = false;
                    buffer.append(line); 
                    //instead of the line above, you could hard-code the ending tag to compensate for bad data:
                    // buffer.append(endTag + ">");

                    try { // to parse as XML
                        builder = factory.newDocumentBuilder();
                        Document document = builder.parse(new InputSource(new StringReader(buffer.toString())));
                        good.add(document); // parsed successfully, add it to the good list

                        buffer.setLength(0); //reset the buffer to start a new XML doc

                    } catch (SAXException ex) {
                        bad.add(buffer.toString()); // something is wrong, not well-formed XML
                    }
                }

                if (append) { // accumulate content
                    buffer.append(line);
                }
            }
            System.out.println("Good items: " + good.size() + " Bad items: " + bad.size());
            //do stuff with the good/bad results...
        }
    }

    public static void main(String args[]) 
      throws ParserConfigurationException, IOException {
        File file = new File("/tmp/test.xml");
        parseFile(file, "Product");
    }

}