diff --git a/src/_pytest/runner.py b/src/_pytest/runner.py
index 6dd8e6c40..7ecc5bbeb 100644
--- a/src/_pytest/runner.py
+++ b/src/_pytest/runner.py
@@ -131,6 +131,12 @@ def runtestprotocol(
             show_test_item(item)
         if not item.config.getoption("setuponly", False):
             reports.append(call_and_report(item, "call", log))
+
+    # If the session is about to fail or stop, teardown everything - this is
+    # necessary to correctly report fixture teardown errors (see #11706)
+    if item.session.shouldfail or item.session.shouldstop:
+        nextitem = None
+
     reports.append(call_and_report(item, "teardown", log, nextitem=nextitem))
     # After all teardown hooks have been called
     # want funcargs and request info to go away.
@@ -179,9 +185,6 @@ def pytest_runtest_call(item: Item) -> None:
 
 def pytest_runtest_teardown(item: Item, nextitem: Optional[Item]) -> None:
     _update_current_test_var(item, "teardown")
-    # If the session is about to fail, teardown everything - this is necessary
-    # to correctly report fixture teardown errors (see #11706)
-    nextitem = None if item.session.shouldfail else nextitem
     item.session._setupstate.teardown_exact(nextitem)
     _update_current_test_var(item, None)