diff --git a/distributed/client.py b/distributed/client.py
index ad283a352a..0601b0db5f 100644
--- a/distributed/client.py
+++ b/distributed/client.py
@@ -5409,8 +5409,7 @@ async def _unregister_worker_plugin(self, name, nanny=None):
 
         for response in responses.values():
             if response["status"] == "error":
-                exc = response["exception"]
-                tb = response["traceback"]
+                _, exc, tb = clean_exception(**response)
                 raise exc.with_traceback(tb)
         return responses
 
diff --git a/distributed/diagnostics/tests/test_nanny_plugin.py b/distributed/diagnostics/tests/test_nanny_plugin.py
index 7906e9a066..3c481dce26 100644
--- a/distributed/diagnostics/tests/test_nanny_plugin.py
+++ b/distributed/diagnostics/tests/test_nanny_plugin.py
@@ -170,7 +170,7 @@ def setup(self, nanny):
 
 
 @gen_cluster(client=True, nthreads=[("", 1)], Worker=Nanny)
-async def test_register_plugin_with_broken_setup_to_existing_nanny_raises(c, s, a):
+async def test_register_plugin_with_broken_setup_to_existing_nannies_raises(c, s, a):
     with pytest.raises(RuntimeError, match="test error"):
         with captured_logger("distributed.nanny", level=logging.ERROR) as caplog:
             await c.register_plugin(BrokenSetupPlugin(), name="TestPlugin1")
@@ -189,3 +189,31 @@ async def test_plugin_with_broken_setup_on_new_nanny_logs(c, s):
     logs = caplog.getvalue()
     assert "TestPlugin1 failed to setup" in logs
     assert "test error" in logs
+
+
+class BrokenTeardownPlugin(NannyPlugin):
+    def teardown(self, nanny):
+        raise RuntimeError("test error")
+
+
+@gen_cluster(client=True, nthreads=[("", 1)], Worker=Nanny)
+async def test_unregister_nanny_plugin_with_broken_teardown_raises(c, s, a):
+    await c.register_plugin(BrokenTeardownPlugin(), name="TestPlugin1")
+    with pytest.raises(RuntimeError, match="test error"):
+        with captured_logger("distributed.nanny", level=logging.ERROR) as caplog:
+            await c.unregister_worker_plugin("TestPlugin1", nanny=True)
+    logs = caplog.getvalue()
+    assert "TestPlugin1 failed to teardown" in logs
+    assert "test error" in logs
+
+
+@gen_cluster(client=True, nthreads=[])
+async def test_nanny_plugin_with_broken_teardown_logs_on_close(c, s):
+    await c.register_plugin(BrokenTeardownPlugin(), name="TestPlugin1")
+
+    with captured_logger("distributed.nanny", level=logging.ERROR) as caplog:
+        async with Nanny(s.address):
+            pass
+    logs = caplog.getvalue()
+    assert "TestPlugin1 failed to teardown" in logs
+    assert "test error" in logs
diff --git a/distributed/nanny.py b/distributed/nanny.py
index 711dd804e9..7a14ee6576 100644
--- a/distributed/nanny.py
+++ b/distributed/nanny.py
@@ -484,7 +484,7 @@ async def plugin_add(
                 if isawaitable(result):
                     result = await result
             except Exception as e:
-                logger.exception("Worker plugin %s failed to setup", name)
+                logger.exception("Nanny plugin %s failed to setup", name)
                 return error_message(e)
         if getattr(plugin, "restart", False):
             await self.restart(reason=f"nanny-plugin-{name}-restart")
@@ -501,6 +501,7 @@ async def plugin_remove(self, name: str) -> ErrorMessage | OKMessage:
                 if isawaitable(result):
                     result = await result
         except Exception as e:
+            logger.exception("Nanny plugin %s failed to teardown", name)
             msg = error_message(e)
             return msg
 
@@ -611,13 +612,7 @@ async def close(  # type:ignore[override]
 
         await self.preloads.teardown()
 
-        teardowns = [
-            plugin.teardown(self)
-            for plugin in self.plugins.values()
-            if hasattr(plugin, "teardown")
-        ]
-
-        await asyncio.gather(*(td for td in teardowns if isawaitable(td)))
+        await asyncio.gather(*(self.plugin_remove(name) for name in self.plugins))
 
         self.stop()
         if self.process is not None: