diff --git a/web/app.js b/web/app.js
index 3a66de48a..a7df2b857 100644
--- a/web/app.js
+++ b/web/app.js
@@ -802,7 +802,19 @@ const PDFViewerApplication = {
     }
 
     if (!this.pdfLoadingTask) {
-      return undefined;
+      return;
+    }
+    if (
+      (typeof PDFJSDev === "undefined" || PDFJSDev.test("GENERIC")) &&
+      this.pdfDocument?.annotationStorage.size > 0 &&
+      this._annotationStorageModified
+    ) {
+      try {
+        // Trigger saving, to prevent data loss in forms; see issue 12257.
+        await this.save({ sourceEventType: "save" });
+      } catch (reason) {
+        // Ignoring errors, to ensure that document closing won't break.
+      }
     }
     const promises = [];
 
@@ -851,8 +863,6 @@ const PDFViewerApplication = {
       PDFBug.cleanup();
     }
     await Promise.all(promises);
-
-    return undefined;
   },
 
   /**
@@ -949,62 +959,59 @@ const PDFViewerApplication = {
     );
   },
 
-  download({ sourceEventType = "download" } = {}) {
-    function downloadByUrl() {
-      downloadManager.downloadUrl(url, filename);
-    }
-
-    const downloadManager = this.downloadManager,
-      url = this.baseUrl,
-      filename = this._docFilename;
-
-    // When the PDF document isn't ready, or the PDF file is still downloading,
-    // simply download using the URL.
-    if (!this.pdfDocument || !this.downloadComplete) {
-      downloadByUrl();
+  /**
+   * @private
+   */
+  _ensureDownloadComplete() {
+    if (this.pdfDocument && this.downloadComplete) {
       return;
     }
+    throw new Error("PDF document not downloaded.");
+  },
 
-    this.pdfDocument
-      .getData()
-      .then(function (data) {
-        const blob = new Blob([data], { type: "application/pdf" });
-        downloadManager.download(blob, url, filename, sourceEventType);
-      })
-      .catch(downloadByUrl); // Error occurred, try downloading with the URL.
+  async download({ sourceEventType = "download" } = {}) {
+    const url = this.baseUrl,
+      filename = this._docFilename;
+    try {
+      this._ensureDownloadComplete();
+
+      const data = await this.pdfDocument.getData();
+      const blob = new Blob([data], { type: "application/pdf" });
+
+      await this.downloadManager.download(blob, url, filename, sourceEventType);
+    } catch (reason) {
+      // When the PDF document isn't ready, or the PDF file is still
+      // downloading, simply download using the URL.
+      await this.downloadManager.downloadUrl(url, filename);
+    }
   },
 
   async save({ sourceEventType = "download" } = {}) {
     if (this._saveInProgress) {
       return;
     }
-
-    const downloadManager = this.downloadManager,
-      url = this.baseUrl,
-      filename = this._docFilename;
-
-    // When the PDF document isn't ready, or the PDF file is still downloading,
-    // simply download using the URL.
-    if (!this.pdfDocument || !this.downloadComplete) {
-      this.download({ sourceEventType });
-      return;
-    }
     this._saveInProgress = true;
     await this.pdfScriptingManager.dispatchWillSave();
 
-    this.pdfDocument
-      .saveDocument(this.pdfDocument.annotationStorage)
-      .then(data => {
-        const blob = new Blob([data], { type: "application/pdf" });
-        downloadManager.download(blob, url, filename, sourceEventType);
-      })
-      .catch(() => {
-        this.download({ sourceEventType });
-      })
-      .finally(async () => {
-        await this.pdfScriptingManager.dispatchDidSave();
-        this._saveInProgress = false;
-      });
+    const url = this.baseUrl,
+      filename = this._docFilename;
+    try {
+      this._ensureDownloadComplete();
+
+      const data = await this.pdfDocument.saveDocument(
+        this.pdfDocument.annotationStorage
+      );
+      const blob = new Blob([data], { type: "application/pdf" });
+
+      await this.downloadManager.download(blob, url, filename, sourceEventType);
+    } catch (reason) {
+      // When the PDF document isn't ready, or the PDF file is still
+      // downloading, simply fallback to a "regular" download.
+      await this.download({ sourceEventType });
+    } finally {
+      await this.pdfScriptingManager.dispatchDidSave();
+      this._saveInProgress = false;
+    }
   },
 
   downloadOrSave(options) {
@@ -1710,11 +1717,19 @@ const PDFViewerApplication = {
     }
     const { annotationStorage } = pdfDocument;
 
-    annotationStorage.onSetModified = function () {
+    annotationStorage.onSetModified = () => {
       window.addEventListener("beforeunload", beforeUnload);
+
+      if (typeof PDFJSDev === "undefined" || PDFJSDev.test("GENERIC")) {
+        this._annotationStorageModified = true;
+      }
     };
-    annotationStorage.onResetModified = function () {
+    annotationStorage.onResetModified = () => {
       window.removeEventListener("beforeunload", beforeUnload);
+
+      if (typeof PDFJSDev === "undefined" || PDFJSDev.test("GENERIC")) {
+        delete this._annotationStorageModified;
+      }
     };
   },