diff --git a/src/display/api.js b/src/display/api.js
index ba5dd87cf8ee0..48de0601c4f48 100644
--- a/src/display/api.js
+++ b/src/display/api.js
@@ -2127,6 +2127,10 @@ class WorkerTransport {
     this.setupMessageHandler();
   }
 
+  get loadingTaskSettled() {
+    return this.loadingTask._capability.settled;
+  }
+
   destroy() {
     if (this.destroyCapability) {
       return this.destroyCapability.promise;
@@ -2154,6 +2158,18 @@ class WorkerTransport {
     // We also need to wait for the worker to finish its long running tasks.
     const terminated = this.messageHandler.sendWithPromise("Terminate", null);
     waitOn.push(terminated);
+    // Allow `AnnotationStorage`-related clean-up when destroying the document.
+    if (this.loadingTaskSettled) {
+      const annotationStorageResetModified = this.loadingTask.promise
+        .then(pdfDocument => {
+          // Avoid initializing the `annotationStorage` if it doesn't exist.
+          if (pdfDocument.hasOwnProperty("annotationStorage")) {
+            pdfDocument.annotationStorage.resetModified();
+          }
+        })
+        .catch(() => {});
+      waitOn.push(annotationStorageResetModified);
+    }
     Promise.all(waitOn).then(() => {
       this.commonObjs.clear();
       this.fontLoader.clear();
diff --git a/web/app.js b/web/app.js
index df37f0c669778..80a67da559787 100644
--- a/web/app.js
+++ b/web/app.js
@@ -1060,6 +1060,14 @@ const PDFViewerApplication = {
       });
   },
 
+  downloadOrSave(options) {
+    if (this.pdfDocument?.annotationStorage.size > 0) {
+      this.save(options);
+    } else {
+      this.download(options);
+    }
+  },
+
   /**
    * For PDF documents that contain e.g. forms and javaScript, we should only
    * trigger the fallback bar once the user has interacted with the page.
@@ -1279,14 +1287,6 @@ const PDFViewerApplication = {
     this.pdfLinkService.setDocument(pdfDocument, baseDocumentUrl);
     this.pdfDocumentProperties.setDocument(pdfDocument, this.url);
 
-    const annotationStorage = pdfDocument.annotationStorage;
-    annotationStorage.onSetModified = function () {
-      window.addEventListener("beforeunload", beforeUnload);
-    };
-    annotationStorage.onResetModified = function () {
-      window.removeEventListener("beforeunload", beforeUnload);
-    };
-
     const pdfViewer = this.pdfViewer;
     pdfViewer.setDocument(pdfDocument);
     const { firstPagePromise, onePageRendered, pagesPromise } = pdfViewer;
@@ -1314,6 +1314,7 @@ const PDFViewerApplication = {
 
     firstPagePromise.then(pdfPage => {
       this.loadingBar.setWidth(this.appConfig.viewerContainer);
+      this._initializeAnnotationStorageCallbacks(pdfDocument);
 
       Promise.all([
         animationStarted,
@@ -1870,6 +1871,23 @@ const PDFViewerApplication = {
     }
   },
 
+  /**
+   * @private
+   */
+  _initializeAnnotationStorageCallbacks(pdfDocument) {
+    if (pdfDocument !== this.pdfDocument) {
+      return;
+    }
+    const { annotationStorage } = pdfDocument;
+
+    annotationStorage.onSetModified = function () {
+      window.addEventListener("beforeunload", beforeUnload);
+    };
+    annotationStorage.onResetModified = function () {
+      window.removeEventListener("beforeunload", beforeUnload);
+    };
+  },
+
   setInitialView(
     storedHash,
     { rotation, sidebarView, scrollMode, spreadMode } = {}
@@ -2712,21 +2730,11 @@ function webViewerPresentationMode() {
 function webViewerPrint() {
   PDFViewerApplication.triggerPrinting();
 }
-function webViewerDownloadOrSave(sourceEventType) {
-  if (
-    PDFViewerApplication.pdfDocument &&
-    PDFViewerApplication.pdfDocument.annotationStorage.size > 0
-  ) {
-    PDFViewerApplication.save({ sourceEventType });
-  } else {
-    PDFViewerApplication.download({ sourceEventType });
-  }
-}
 function webViewerDownload() {
-  webViewerDownloadOrSave("download");
+  PDFViewerApplication.downloadOrSave({ sourceEventType: "download" });
 }
 function webViewerSave() {
-  webViewerDownloadOrSave("save");
+  PDFViewerApplication.downloadOrSave({ sourceEventType: "save" });
 }
 function webViewerFirstPage() {
   if (PDFViewerApplication.pdfDocument) {