diff --git a/docs/search.js b/docs/search.js
index 83615f0ca96..a82d79669a2 100644
--- a/docs/search.js
+++ b/docs/search.js
@@ -122,13 +122,13 @@ async function run() {
   await Content.deleteMany({ version });
   for (const content of contents) {
     if (version !== '6.x') {
-      content.url = `/docs/${version}/docs/${content.url}`;
+      content.url = `/docs/${version}/docs${content.url}`;
     }
     await content.save();
   }
 
   const results = await Content.
-    find({ $text: { $search: 'validate' } }, { score: { $meta: 'textScore' } }).
+    find({ $text: { $search: 'validate' }, version }, { score: { $meta: 'textScore' } }).
     sort({ score: { $meta: 'textScore' } }).
     limit(10);
 
diff --git a/lib/helpers/query/castUpdate.js b/lib/helpers/query/castUpdate.js
index 50d56509610..2e1dde1a6c0 100644
--- a/lib/helpers/query/castUpdate.js
+++ b/lib/helpers/query/castUpdate.js
@@ -85,9 +85,11 @@ module.exports = function castUpdate(schema, obj, options, context, filter) {
     val = ret[op];
     hasDollarKey = hasDollarKey || op.startsWith('$');
     const toUnset = {};
-    for (const key of Object.keys(val)) {
-      if (val[key] === undefined) {
-        toUnset[key] = 1;
+    if (val != null) {
+      for (const key of Object.keys(val)) {
+        if (val[key] === undefined) {
+          toUnset[key] = 1;
+        }
       }
     }
 
diff --git a/test/query.test.js b/test/query.test.js
index f291c5d226f..a02a37896d0 100644
--- a/test/query.test.js
+++ b/test/query.test.js
@@ -4314,7 +4314,7 @@ describe('Query', function() {
     assert.strictEqual(found[0].title, 'burrito bowl');
   });
 
-  it('update operation should remove fields set to undefined (gh-12794)', async() => {
+  it('update operation should remove fields set to undefined (gh-12794) (gh-12821)', async function() {
     const m = new mongoose.Mongoose();
 
     await m.connect(start.uri);
@@ -4338,5 +4338,15 @@ describe('Query', function() {
     ).lean();
 
     assert.ok('title' in updatedDoc === false);
+
+    const replacedDoc = await Test.findOneAndReplace(
+      {
+        _id: doc._id
+      },
+      { title: undefined },
+      { returnOriginal: false }
+    ).lean();
+
+    assert.ok('title' in replacedDoc === false);
   });
 });
diff --git a/test/schema.test.js b/test/schema.test.js
index 67e678fa184..dec8be82d56 100644
--- a/test/schema.test.js
+++ b/test/schema.test.js
@@ -2833,7 +2833,7 @@ describe('schema', function() {
     assert.equal(entry instanceof mongoose.Document, false);
   });
 
-  it('disallows setting special properties with `add()` or constructor (gh-12085)', async function() {
+  it('disallows setting special properties with `add()` or constructor (gh-12085)', function() {
     const maliciousPayload = '{"__proto__.toString": "Number"}';
 
     assert.throws(() => {