diff --git a/synapse/http/server.py b/synapse/http/server.py
index 2c235e04f4..a0ae20be16 100644
--- a/synapse/http/server.py
+++ b/synapse/http/server.py
@@ -33,6 +33,7 @@ from typing import (
     Any,
     Awaitable,
     Callable,
+    Final,
     Iterable,
     Iterator,
     Pattern,
@@ -673,8 +674,33 @@ class UnrecognizedRequestResource(resource.Resource):
         # or the response bytes as a return value.
         return NOT_DONE_YET
 
-    def getChild(self, name: str, request: Request) -> resource.Resource:
-        return self
+    def getChild(self, path: str, request: Request) -> resource.Resource:
+        # The child of a catch-all unrecognised request handler
+        # is itself another unrecognised request handler.
+        # We can return any UnrecognizedRequestResource that doesn't
+        # have children.
+        assert len(_BLANK_LEAF_UNRECOGNISED_REQUEST_RESOURCE.children) == 0
+        return _BLANK_LEAF_UNRECOGNISED_REQUEST_RESOURCE
+
+
+class _LeafUnrecognisedRequestResource(UnrecognizedRequestResource):
+    """
+    UnrecognizedRequestResource, but with the added caveat that it can't have any children.
+    This makes it safe for it to return itself as a dynamic child.
+
+    Constructed as a singleton; use `_BLANK_LEAF_UNRECOGNISED_REQUEST_RESOURCE`
+    """
+
+    def putChild(self, path: bytes, child: IResource) -> None:
+        raise RuntimeError("_LeafUnrecognisedRequestResource does not accept children")
+
+
+_BLANK_LEAF_UNRECOGNISED_REQUEST_RESOURCE: Final[_LeafUnrecognisedRequestResource] = (
+    _LeafUnrecognisedRequestResource()
+)
+"""
+An UnrecognizedRequestResource that is guaranteed not to have children.
+"""
 
 
 class RootRedirect(resource.Resource):
diff --git a/tests/util/test_httpresourcetree.py b/tests/util/test_httpresourcetree.py
new file mode 100644
index 0000000000..b5dc2e0657
--- /dev/null
+++ b/tests/util/test_httpresourcetree.py
@@ -0,0 +1,66 @@
+#
+# This file is licensed under the Affero General Public License (AGPL) version 3.
+#
+# Copyright (C) 2026 Element Creations Ltd
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU Affero General Public License as
+# published by the Free Software Foundation, either version 3 of the
+# License, or (at your option) any later version.
+#
+# See the GNU Affero General Public License for more details:
+# <https://www.gnu.org/licenses/agpl-3.0.html>.
+#
+import os
+from http import HTTPStatus
+
+from twisted.web.resource import Resource
+
+import synapse
+from synapse.api.errors import Codes
+from synapse.api.urls import STATIC_PREFIX
+from synapse.http.server import StaticResource
+
+from tests import unittest
+
+
+class ResourceTreeTestCase(unittest.HomeserverTestCase):
+    servlets = []
+
+    def create_resource_dict(self) -> dict[str, Resource]:
+        """
+        Register /_matrix/static for the test.
+        """
+        resources = super().create_resource_dict()
+        resources[STATIC_PREFIX] = StaticResource(
+            # as in `synapse/app/homeserver.py` `_configure_named_resource`
+            os.path.join(os.path.dirname(synapse.__file__), "static")
+        )
+        return resources
+
+    def test_inserted_segment_is_silently_swallowed(self) -> None:
+        """
+        Regression test for https://github.com/element-hq/synapse/security/advisories/GHSA-vh4c-pqh4-w3wq
+
+        The path `/_matrix/INSERTED/static/client/login/style.css` used to resolve to the same
+        as `/_matrix/static/client/login/style.css`.
+        """
+        PATH_SUFFIX = "/static/client/login/style.css"
+        correct_channel = self.make_request(
+            "GET",
+            f"/_matrix{PATH_SUFFIX}",
+            shorthand=False,
+        )
+        # The correct path should give a 200 OK static resource
+        self.assertEqual(correct_channel.code, HTTPStatus.OK, correct_channel.result)
+
+        wrong_channel = self.make_request(
+            "GET",
+            f"/_matrix/INSERTED{PATH_SUFFIX}",
+            shorthand=False,
+        )
+        # This prefixed version of the same path should give a 404
+        self.assertEqual(wrong_channel.code, HTTPStatus.NOT_FOUND, wrong_channel.result)
+        self.assertEqual(
+            wrong_channel.json_body["errcode"], Codes.UNRECOGNIZED, wrong_channel.result
+        )