ADDITIONAL SYSTEM INFORMATION :
Tested on Windows but the OS is likely irrelevant. Reproduced with Java 8, 11, 17, and current 21 early access.

A DESCRIPTION OF THE PROBLEM :
The EntityResolver2.getExternalSubset() [1] apidoc states:

> Allows applications to provide an external subset for documents that
> don't explicitly define one. Documents with DOCTYPE declarations that
> omit an external subset can thus augment the declarations available
> for validation, entity processing, and attribute processing
> (normalization, defaulting, and reporting types including ID).
>
> This method can also be used with documents that have no DOCTYPE
> declaration. When the root element is encountered, but no DOCTYPE
> declaration has been seen, this method is invoked.

However, it doesn't appear to be the case with documents that have no DOCTYPE declaration. Additionally, for documents that have a DOCTYPE declaration and specify an internal subset, the supplied external subset appears to be ignored.

I've found an existing:

* https://bugs.openjdk.org/browse/JDK-6524460 "EntityResolver2 no longer used in Java6"

It describes the first case – getExternalSubset() never invoked for documents that have no DOCTYPE declaration. I've also identified a conflict with the internal subset when defined. FWIW, both of these cases work as expected using the original Xerces2 implementation.

[1]: https://docs.oracle.com/en/java/javase/11/docs/api/java.xml/org/xml/sax/ext/EntityResolver2.html#getExternalSubset(java.lang.String,java.lang.String)

STEPS TO FOLLOW TO REPRODUCE THE PROBLEM :
> java SAXParserProvidedExternalSubsetTest
> java DOMBuilderProvidedExternalSubsetTest


EXPECTED VERSUS ACTUAL BEHAVIOR :
EXPECTED -
Output (no errors):

doctype-no-ext-subset.xml
no-doctype-decl.xml
doctype-int-subset.xml
ACTUAL -
> java SAXParserProvidedExternalSubsetTest
doctype-no-ext-subset.xml
no-doctype-decl.xml
org.xml.sax.SAXParseException; systemId: file:/.../no-doctype-decl.xml; lineNumber: 4; columnNumber: 13; The entity "nbsp" was referenced, but not declared.
        at java.xml/com.sun.org.apache.xerces.internal.parsers.AbstractSAXParser.parse(AbstractSAXParser.java:1243)
        at java.xml/com.sun.org.apache.xerces.internal.jaxp.SAXParserImpl$JAXPSAXParser.parse(SAXParserImpl.java:635)
        at SAXParserProvidedExternalSubsetTest.testExternalSubsetRequested(SAXParserProvidedExternalSubsetTest.java:47)
        at SAXParserProvidedExternalSubsetTest.testNoDoctype(SAXParserProvidedExternalSubsetTest.java:30)
        at SAXParserProvidedExternalSubsetTest.run(SAXParserProvidedExternalSubsetTest.java:86)
        at SAXParserProvidedExternalSubsetTest.main(SAXParserProvidedExternalSubsetTest.java:76)
doctype-int-subset.xml
java.lang.AssertionError: Expected text content: "Foo   Bar™", but was: "Foo Bar™"
        at SAXParserProvidedExternalSubsetTest.assertEquals(SAXParserProvidedExternalSubsetTest.java:66)
        at SAXParserProvidedExternalSubsetTest.testExternalSubsetRequested(SAXParserProvidedExternalSubsetTest.java:51)
        at SAXParserProvidedExternalSubsetTest.testDoctypeWithIntSubset(SAXParserProvidedExternalSubsetTest.java:34)
        at SAXParserProvidedExternalSubsetTest.run(SAXParserProvidedExternalSubsetTest.java:86)
        at SAXParserProvidedExternalSubsetTest.main(SAXParserProvidedExternalSubsetTest.java:77)

> java DOMBuilderProvidedExternalSubsetTest
doctype-no-ext-subset.xml
no-doctype-decl.xml
org.xml.sax.SAXParseException; systemId: file:/.../no-doctype-decl.xml; lineNumber: 4; columnNumber: 13; The entity "nbsp" was referenced, but not declared.
        at java.xml/com.sun.org.apache.xerces.internal.parsers.DOMParser.parse(DOMParser.java:261)
        at java.xml/com.sun.org.apache.xerces.internal.jaxp.DocumentBuilderImpl.parse(DocumentBuilderImpl.java:339)
        at DOMBuilderProvidedExternalSubsetTest.testExternalSubsetRequested(DOMBuilderProvidedExternalSubsetTest.java:49)
        at DOMBuilderProvidedExternalSubsetTest.testNoDoctype(DOMBuilderProvidedExternalSubsetTest.java:33)
        at DOMBuilderProvidedExternalSubsetTest.run(DOMBuilderProvidedExternalSubsetTest.java:87)
        at DOMBuilderProvidedExternalSubsetTest.main(DOMBuilderProvidedExternalSubsetTest.java:77)
doctype-int-subset.xml
java.lang.AssertionError: Expected text content: "Foo   Bar™", but was: ""
        at DOMBuilderProvidedExternalSubsetTest.assertEquals(DOMBuilderProvidedExternalSubsetTest.java:67)
        at DOMBuilderProvidedExternalSubsetTest.testExternalSubsetRequested(DOMBuilderProvidedExternalSubsetTest.java:52)
        at DOMBuilderProvidedExternalSubsetTest.testDoctypeWithIntSubset(DOMBuilderProvidedExternalSubsetTest.java:37)
        at DOMBuilderProvidedExternalSubsetTest.run(DOMBuilderProvidedExternalSubsetTest.java:87)
        at DOMBuilderProvidedExternalSubsetTest.main(DOMBuilderProvidedExternalSubsetTest.java:78)


---------- BEGIN SOURCE ----------
---doctype-no-ext-subset.xml
<!DOCTYPE html>
<html>
<body>
  Foo &nbsp; Bar&#x2122;
</body>
</html>
---doctype-no-ext-subset.xml--

---no-doctype-decl.xml
<?xml version="1.0" encoding="UTF-8"?>
<html xmlns="http://www.w3.org/1999/xhtml">
<body>
  Foo &nbsp; Bar&#x2122;
</body>
</html>
---no-doctype-decl.xml--

---doctype-int-subset.xml
<!DOCTYPE html [
  <!ENTITY trade "&#x2122;">
]>
<html>
<body>
  Foo &nbsp; Bar&trade;
</body>
</html>
---doctype-int-subset.xml--

---SAXParserProvidedExternalSubsetTest.java
//package ;

import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.StringReader;
import java.net.URL;
import java.util.Objects;

import javax.xml.parsers.SAXParserFactory;
import org.xml.sax.InputSource;
import org.xml.sax.SAXException;
import org.xml.sax.SAXParseException;
import org.xml.sax.XMLReader;
import org.xml.sax.ext.DefaultHandler2;

public class SAXParserProvidedExternalSubsetTest {

    private SAXParserFactory parserFactory;

    public void setUp() throws Exception {
        parserFactory = SAXParserFactory.newInstance();
        parserFactory.setNamespaceAware(true);
    }

    public void testDoctypeNoExternalSubset() throws Exception {
        testExternalSubsetRequested("doctype-no-ext-subset.xml");
    }

    public void testNoDoctype() throws Exception {
        testExternalSubsetRequested("no-doctype-decl.xml");
    }

    public void testDoctypeWithIntSubset() throws Exception {
        testExternalSubsetRequested("doctype-int-subset.xml");
    }

    private void testExternalSubsetRequested(String resource) throws Exception {
        System.out.println(resource);

        XMLReader xmlReader = parserFactory.newSAXParser().getXMLReader();
        TestHandler testHandler = new TestHandler();
        xmlReader.setErrorHandler(testHandler);
        xmlReader.setEntityResolver(testHandler);
        xmlReader.setContentHandler(testHandler);

        InputSource source = new InputSource(getResource(resource).toString());
        xmlReader.parse(source);

        assertEquals("requested external subset",
                testHandler.requestedExternalSubset, "html");
        assertEquals("text content",
                testHandler.textContent.toString().trim(), "Foo \u00A0 Bar\u2122");
    }

    private static URL getResource(String name) throws IOException {
        URL resource = SAXParserProvidedExternalSubsetTest.class.getResource(name);
        if (resource == null) {
            throw new FileNotFoundException("Resource not found: " + name);
        }
        return resource;
    }

    private static void assertEquals(String subject, String actual, String expected)
            throws AssertionError {
        if (!Objects.equals(actual, expected)) {
            throw new AssertionError("Expected " + subject
                    + ": \"" + expected + "\", but was: \"" + actual + "\"");
        }
    }

    public static void main(String[] args) throws Exception {
        SAXParserProvidedExternalSubsetTest
                suite = new SAXParserProvidedExternalSubsetTest();
        suite.setUp();
        if (run(suite::testDoctypeNoExternalSubset)
                & run(suite::testNoDoctype)
                & run(suite::testDoctypeWithIntSubset)) {
            // success
        } else {
            System.exit(1);
        }
    }

    private static boolean run(ThrowingRunnable testCase) {
        try {
            testCase.run();
            return true;
        } catch (Throwable e) {
            e.printStackTrace();
            return false;
        }
    }


    @FunctionalInterface
    static interface ThrowingRunnable {
        void run() throws Throwable;
    }


    static class TestHandler extends DefaultHandler2 {

        String requestedExternalSubset;

        StringBuilder textContent = new StringBuilder();

        private static InputSource htmlEntities() {
            return new InputSource(new StringReader("<!ENTITY nbsp '&#xA0;'>"));
        }

        @Override
        public InputSource getExternalSubset(String name, String baseURI)
                throws SAXException, IOException {
            requestedExternalSubset = name;
            return "html".equals(name) ? htmlEntities() : null;
        }

        @Override
        public void characters(char[] ch, int start, int length)
                throws SAXException {
            textContent.append(ch, start, length);
        }

        @Override
        public void warning(SAXParseException e) throws SAXException {
            System.err.append("[warning] ").println(e);
        }

        @Override
        public void error(SAXParseException e) throws SAXException {
            System.err.append("[error] ").println(e);
        }

        @Override
        public void fatalError(SAXParseException e) throws SAXException {
            // Parser should signal an exception in any case
        }

    } // class TestHandler


} // class SAXParserProvidedExternalSubsetTest
---SAXParserProvidedExternalSubsetTest.java--

---DOMBuilderProvidedExternalSubsetTest.java
//package ;

import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.StringReader;
import java.net.URL;
import java.util.Objects;

import javax.xml.parsers.DocumentBuilder;
import javax.xml.parsers.DocumentBuilderFactory;
import org.w3c.dom.Document;
import org.w3c.dom.Node;
import org.xml.sax.InputSource;
import org.xml.sax.SAXException;
import org.xml.sax.SAXParseException;
import org.xml.sax.ext.DefaultHandler2;

public class DOMBuilderProvidedExternalSubsetTest {

    private DocumentBuilderFactory parserFactory;

    public void setUp() throws Exception {
        parserFactory = DocumentBuilderFactory.newInstance();
        parserFactory.setNamespaceAware(true);
        //parserFactory.setExpandEntityReferences(false);
    }

    public void testDoctypeNoExternalSubset() throws Exception {
        testExternalSubsetRequested("doctype-no-ext-subset.xml");
    }

    public void testNoDoctype() throws Exception {
        testExternalSubsetRequested("no-doctype-decl.xml");
    }

    public void testDoctypeWithIntSubset() throws Exception {
        testExternalSubsetRequested("doctype-int-subset.xml");
    }

    private void testExternalSubsetRequested(String resource) throws Exception {
        System.out.println(resource);

        DocumentBuilder domBuilder = parserFactory.newDocumentBuilder();
        TestHandler testHandler = new TestHandler();
        domBuilder.setErrorHandler(testHandler);
        domBuilder.setEntityResolver(testHandler);

        InputSource source = new InputSource(getResource(resource).toString());
        Document document = domBuilder.parse(source);

        Node body = document.getElementsByTagName("body").item(0);
        assertEquals("text content",
                body.getTextContent().trim(), "Foo \u00A0 Bar\u2122");
    }

    private static URL getResource(String name) throws IOException {
        URL resource = DOMBuilderProvidedExternalSubsetTest.class.getResource(name);
        if (resource == null) {
            throw new FileNotFoundException("Resource not found: " + name);
        }
        return resource;
    }

    private static void assertEquals(String subject, String actual, String expected)
            throws AssertionError {
        if (!Objects.equals(actual, expected)) {
            throw new AssertionError("Expected " + subject
                    + ": \"" + expected + "\", but was: \"" + actual + "\"");
        }
    }

    public static void main(String[] args) throws Exception {
        DOMBuilderProvidedExternalSubsetTest
                suite = new DOMBuilderProvidedExternalSubsetTest();
        suite.setUp();
        if (run(suite::testDoctypeNoExternalSubset)
                & run(suite::testNoDoctype)
                & run(suite::testDoctypeWithIntSubset)) {
            // success
        } else {
            System.exit(1);
        }
    }

    private static boolean run(ThrowingRunnable testCase) {
        try {
            testCase.run();
            return true;
        } catch (Throwable e) {
            e.printStackTrace();
            return false;
        }
    }


    @FunctionalInterface
    static interface ThrowingRunnable {
        void run() throws Throwable;
    }


    static class TestHandler extends DefaultHandler2 {

        private static InputSource htmlEntities() {
            return new InputSource(new StringReader("<!ENTITY nbsp '&#xA0;'>"));
        }

        @Override
        public InputSource getExternalSubset(String name, String baseURI)
                throws SAXException, IOException {
            return "html".equals(name) ? htmlEntities() : null;
        }

        @Override
        public void warning(SAXParseException e) throws SAXException {
            System.err.append("[warning] ").println(e);
        }

        @Override
        public void error(SAXParseException e) throws SAXException {
            System.err.append("[error] ").println(e);
        }

        @Override
        public void fatalError(SAXParseException e) throws SAXException {
            // Parser should signal an exception in any case
        }

    } // class TestHandler


} // class DOMBuilderProvidedExternalSubsetTest
---DOMBuilderProvidedExternalSubsetTest.java--

---------- END SOURCE ----------

CUSTOMER SUBMITTED WORKAROUND :
Possibly add the original Xerces2 implementation to the runtime.

FREQUENCY : always