diff --git a/src/display/api.js b/src/display/api.js
index 815e7ee23..84f7c2d83 100644
--- a/src/display/api.js
+++ b/src/display/api.js
@@ -629,39 +629,48 @@ const isValidExplicitDest = _isValidExplicitDest.bind(
 class PDFDocumentLoadingTask {
   static #docId = 0;
 
-  constructor() {
-    this._capability = Promise.withResolvers();
-    this._transport = null;
-    this._worker = null;
+  /**
+   * @private
+   */
+  _capability = Promise.withResolvers();
 
-    /**
-     * Unique identifier for the document loading task.
-     * @type {string}
-     */
-    this.docId = `d${PDFDocumentLoadingTask.#docId++}`;
+  /**
+   * @private
+   */
+  _transport = null;
 
-    /**
-     * Whether the loading task is destroyed or not.
-     * @type {boolean}
-     */
-    this.destroyed = false;
+  /**
+   * @private
+   */
+  _worker = null;
 
-    /**
-     * Callback to request a password if a wrong or no password was provided.
-     * The callback receives two parameters: a function that should be called
-     * with the new password, and a reason (see {@link PasswordResponses}).
-     * @type {function}
-     */
-    this.onPassword = null;
+  /**
+   * Unique identifier for the document loading task.
+   * @type {string}
+   */
+  docId = `d${PDFDocumentLoadingTask.#docId++}`;
 
-    /**
-     * Callback to be able to monitor the loading progress of the PDF file
-     * (necessary to implement e.g. a loading bar).
-     * The callback receives an {@link OnProgressParameters} argument.
-     * @type {function}
-     */
-    this.onProgress = null;
-  }
+  /**
+   * Whether the loading task is destroyed or not.
+   * @type {boolean}
+   */
+  destroyed = false;
+
+  /**
+   * Callback to request a password if a wrong or no password was provided.
+   * The callback receives two parameters: a function that should be called
+   * with the new password, and a reason (see {@link PasswordResponses}).
+   * @type {function}
+   */
+  onPassword = null;
+
+  /**
+   * Callback to be able to monitor the loading progress of the PDF file
+   * (necessary to implement e.g. a loading bar).
+   * The callback receives an {@link OnProgressParameters} argument.
+   * @type {function}
+   */
+  onProgress = null;
 
   /**
    * Promise for document loading task completion.
@@ -699,6 +708,16 @@ class PDFDocumentLoadingTask {
     this._worker?.destroy();
     this._worker = null;
   }
+
+  /**
+   * Attempt to fetch the raw data of the PDF document, when e.g.
+   *  - An exception was thrown during document initialization.
+   *  - An `onPassword` callback is delaying initialization.
+   * @returns {Promise<Uint8Array>}
+   */
+  async getData() {
+    return this._transport.getData();
+  }
 }
 
 /**
diff --git a/test/unit/api_spec.js b/test/unit/api_spec.js
index 3acc4c38f..2f0fdc040 100644
--- a/test/unit/api_spec.js
+++ b/test/unit/api_spec.js
@@ -828,6 +828,47 @@ describe("api", function () {
 
       await loadingTask.destroy();
     });
+
+    it("gets data, on failure, from `PDFDocumentLoadingTask`-instance", async function () {
+      const typedArrayPdf = await DefaultFileReaderFactory.fetch({
+        path: TEST_PDFS_PATH + "issue6010_1.pdf",
+      });
+
+      // Sanity check to make sure that we fetched the entire PDF file.
+      expect(typedArrayPdf instanceof Uint8Array).toEqual(true);
+      expect(typedArrayPdf.length).toEqual(1116);
+
+      const loadingTask = getDocument(typedArrayPdf.slice());
+      expect(loadingTask instanceof PDFDocumentLoadingTask).toEqual(true);
+
+      let passwordData = null;
+      // Attach the callback that is used to request a password;
+      // similarly to how the default viewer handles passwords.
+      loadingTask.onPassword = async (updatePassword, reason) => {
+        passwordData = await loadingTask.getData();
+
+        updatePassword(new Error("Should reject the loadingTask."));
+      };
+
+      try {
+        await loadingTask.promise;
+
+        // Shouldn't get here.
+        expect(false).toEqual(true);
+      } catch (ex) {
+        expect(ex instanceof PasswordException).toEqual(true);
+        expect(ex.code).toEqual(PasswordResponses.NEED_PASSWORD);
+      }
+
+      // Ensure that the raw PDF document can be fetched while
+      // an `onPassword` callback is delaying initialization...
+      expect(passwordData).toEqual(typedArrayPdf);
+      // ... and once an exception has stopped initialization.
+      const data = await loadingTask.getData();
+      expect(data).toEqual(typedArrayPdf);
+
+      await loadingTask.destroy();
+    });
   });
 
   describe("PDFWorker", function () {
diff --git a/web/app.js b/web/app.js
index 05cb832f3..eed21ddef 100644
--- a/web/app.js
+++ b/web/app.js
@@ -1153,7 +1153,9 @@ const PDFViewerApplication = {
   async download() {
     let data;
     try {
-      data = await this.pdfDocument.getData();
+      data = await (this.pdfDocument
+        ? this.pdfDocument.getData()
+        : this.pdfLoadingTask.getData());
     } catch {
       // When the PDF document isn't ready, simply download using the URL.
     }