diff --git a/AUTHORS b/AUTHORS
index 14a35c3d5c3..67e794527fb 100644
--- a/AUTHORS
+++ b/AUTHORS
@@ -54,6 +54,7 @@ Aviral Verma
 Aviv Palivoda
 Babak Keyvani
 Barney Gale
+Ben Brown
 Ben Gartner
 Ben Webb
 Benjamin Peterson
diff --git a/changelog/11706.bugfix.rst b/changelog/11706.bugfix.rst
new file mode 100644
index 00000000000..1b90d8f0b60
--- /dev/null
+++ b/changelog/11706.bugfix.rst
@@ -0,0 +1 @@
+Fix reporting of teardown errors in higher-scoped fixtures when using `--maxfail` or `--stepwise`.
diff --git a/src/_pytest/main.py b/src/_pytest/main.py
index 9fb96840e5c..51be84164b2 100644
--- a/src/_pytest/main.py
+++ b/src/_pytest/main.py
@@ -6,6 +6,7 @@
 import importlib
 import os
 import sys
+import warnings
 from pathlib import Path
 from typing import AbstractSet
 from typing import Callable
@@ -44,6 +45,7 @@
 from _pytest.reports import TestReport
 from _pytest.runner import collect_one_node
 from _pytest.runner import SetupState
+from _pytest.warning_types import PytestWarning
 
 
 def pytest_addoption(parser: Parser) -> None:
@@ -548,8 +550,8 @@ def __init__(self, config: Config) -> None:
         )
         self.testsfailed = 0
         self.testscollected = 0
-        self.shouldstop: Union[bool, str] = False
-        self.shouldfail: Union[bool, str] = False
+        self._shouldstop: Union[bool, str] = False
+        self._shouldfail: Union[bool, str] = False
         self.trace = config.trace.root.get("collection")
         self._initialpaths: FrozenSet[Path] = frozenset()
         self._initialpaths_with_parents: FrozenSet[Path] = frozenset()
@@ -576,6 +578,42 @@ def __repr__(self) -> str:
             self.testscollected,
         )
 
+    @property
+    def shouldstop(self) -> Union[bool, str]:
+        return self._shouldstop
+
+    @shouldstop.setter
+    def shouldstop(self, value: Union[bool, str]) -> None:
+        # The runner checks shouldfail and assumes that if it is set we are
+        # definitely stopping, so prevent unsetting it.
+        if value is False and self._shouldstop:
+            warnings.warn(
+                PytestWarning(
+                    "session.shouldstop cannot be unset after it has been set; ignoring."
+                ),
+                stacklevel=2,
+            )
+            return
+        self._shouldstop = value
+
+    @property
+    def shouldfail(self) -> Union[bool, str]:
+        return self._shouldfail
+
+    @shouldfail.setter
+    def shouldfail(self, value: Union[bool, str]) -> None:
+        # The runner checks shouldfail and assumes that if it is set we are
+        # definitely stopping, so prevent unsetting it.
+        if value is False and self._shouldfail:
+            warnings.warn(
+                PytestWarning(
+                    "session.shouldfail cannot be unset after it has been set; ignoring."
+                ),
+                stacklevel=2,
+            )
+            return
+        self._shouldfail = value
+
     @property
     def startpath(self) -> Path:
         """The path from which pytest was invoked.
diff --git a/src/_pytest/runner.py b/src/_pytest/runner.py
index e20338520eb..3e19f0de50c 100644
--- a/src/_pytest/runner.py
+++ b/src/_pytest/runner.py
@@ -131,6 +131,10 @@ 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.
diff --git a/testing/test_runner.py b/testing/test_runner.py
index c8b646857e7..26f5b9a0bc2 100644
--- a/testing/test_runner.py
+++ b/testing/test_runner.py
@@ -1087,3 +1087,53 @@ def func() -> None:
     with pytest.raises(TypeError) as excinfo:
         OutcomeException(func)  # type: ignore
     assert str(excinfo.value) == expected
+
+
+def test_teardown_session_failed(pytester: Pytester) -> None:
+    """Test that higher-scoped fixture teardowns run in the context of the last
+    item after the test session bails early due to --maxfail.
+
+    Regression test for #11706.
+    """
+    pytester.makepyfile(
+        """
+        import pytest
+
+        @pytest.fixture(scope="module")
+        def baz():
+            yield
+            pytest.fail("This is a failing teardown")
+
+        def test_foo(baz):
+            pytest.fail("This is a failing test")
+
+        def test_bar(): pass
+        """
+    )
+    result = pytester.runpytest("--maxfail=1")
+    result.assert_outcomes(failed=1, errors=1)
+
+
+def test_teardown_session_stopped(pytester: Pytester) -> None:
+    """Test that higher-scoped fixture teardowns run in the context of the last
+    item after the test session bails early due to --stepwise.
+
+    Regression test for #11706.
+    """
+    pytester.makepyfile(
+        """
+        import pytest
+
+        @pytest.fixture(scope="module")
+        def baz():
+            yield
+            pytest.fail("This is a failing teardown")
+
+        def test_foo(baz):
+            pytest.fail("This is a failing test")
+
+        def test_bar(): pass
+        """
+    )
+    result = pytester.runpytest("--stepwise")
+    result.assert_outcomes(failed=1, errors=1)
diff --git a/testing/test_session.py b/testing/test_session.py
index 136e85eb640..803bbed5434 100644
--- a/testing/test_session.py
+++ b/testing/test_session.py
@@ -418,3 +418,63 @@ def test_rootdir_wrong_option_arg(pytester: Pytester) -> None:
     result.stderr.fnmatch_lines(
         ["*Directory *wrong_dir* not found. Check your '--rootdir' option.*"]
     )
+
+
+def test_shouldfail_is_sticky(pytester: Pytester) -> None:
+    """Test that session.shouldfail cannot be reset to False after being set.
+
+    Issue #11706.
+    """
+    pytester.makeconftest(
+        """
+        def pytest_sessionfinish(session):
+            assert session.shouldfail
+            session.shouldfail = False
+            assert session.shouldfail
+        """
+    )
+    pytester.makepyfile(
+        """
+        import pytest
+
+        def test_foo():
+            pytest.fail("This is a failing test")
+
+        def test_bar(): pass
+        """
+    )
+
+    result = pytester.runpytest("--maxfail=1", "-Wall")
+
+    result.assert_outcomes(failed=1, warnings=1)
+    result.stdout.fnmatch_lines("*session.shouldfail cannot be unset*")
+
+
+def test_shouldstop_is_sticky(pytester: Pytester) -> None:
+    """Test that session.shouldstop cannot be reset to False after being set.
+
+    Issue #11706.
+    """
+    pytester.makeconftest(
+        """
+        def pytest_sessionfinish(session):
+            assert session.shouldstop
+            session.shouldstop = False
+            assert session.shouldstop
+        """
+    )
+    pytester.makepyfile(
+        """
+        import pytest
+
+        def test_foo():
+            pytest.fail("This is a failing test")
+
+        def test_bar(): pass
+        """
+    )
+
+    result = pytester.runpytest("--stepwise", "-Wall")
+
+    result.assert_outcomes(failed=1, warnings=1)
+    result.stdout.fnmatch_lines("*session.shouldstop cannot be unset*")