diff --git a/distributed/comm/tcp.py b/distributed/comm/tcp.py
index d88582bc67c..03f23116018 100644
--- a/distributed/comm/tcp.py
+++ b/distributed/comm/tcp.py
@@ -240,11 +240,12 @@ async def read(self, deserializers=None):
             self._closed = True
             if not sys.is_finalizing():
                 convert_stream_closed_error(self, e)
-        except Exception:
-            # Some OSError or a another "low-level" exception. We do not really know what
-            # was already read from the underlying socket, so it is not even safe to retry
-            # here using the same stream. The only safe thing to do is to abort.
-            # (See also GitHub #4133).
+        except BaseException:
+            # Some OSError, CancelledError or a another "low-level" exception.
+            # We do not really know what was already read from the underlying
+            # socket, so it is not even safe to retry here using the same stream.
+            # The only safe thing to do is to abort.
+            # (See also GitHub #4133, #6548).
             self.abort()
             raise
         else:
@@ -317,11 +318,14 @@ async def write(self, msg, serializers=None, on_error="message"):
             self._closed = True
             if not sys.is_finalizing():
                 convert_stream_closed_error(self, e)
-        except Exception:
+        except BaseException:
             # Some OSError or a another "low-level" exception. We do not really know
             # what was already written to the underlying socket, so it is not even safe
             # to retry here using the same stream. The only safe thing to do is to
             # abort. (See also GitHub #4133).
+            # In case of, for instance, KeyboardInterrupts or other
+            # BaseExceptions that could be handled further upstream, we equally
+            # want to discard this comm
             self.abort()
             raise
 
diff --git a/distributed/comm/tests/test_comms.py b/distributed/comm/tests/test_comms.py
index fae1e5b6d23..cff48105dea 100644
--- a/distributed/comm/tests/test_comms.py
+++ b/distributed/comm/tests/test_comms.py
@@ -857,8 +857,15 @@ async def handle_comm(comm):
     await comm.close()
 
 
+class CustomBase(BaseException):
+    # We don't want to interfere with KeyboardInterrupts or CancelledErrors for
+    # this test
+    ...
+
+
+@pytest.mark.parametrize("exc_type", [BufferError, CustomBase])
 @gen_test()
-async def test_comm_closed_on_buffer_error(tcp):
+async def test_comm_closed_on_write_error(tcp, exc_type):
     # Internal errors from comm.stream.write, such as
     # BufferError should lead to the stream being closed
     # and not re-used. See GitHub #4133
@@ -868,12 +875,29 @@ async def test_comm_closed_on_buffer_error(tcp):
     reader, writer = await get_tcp_comm_pair()
 
     def _write(data):
-        raise BufferError
+        raise exc_type()
 
     writer.stream.write = _write
-    with pytest.raises(BufferError):
+    with pytest.raises(exc_type):
         await writer.write("x")
-    assert writer.stream is None
+
+    assert writer.closed()
+
+    await reader.close()
+    await writer.close()
+
+
+@gen_test()
+async def test_comm_closed_on_read_error(tcp):
+    if tcp is asyncio_tcp:
+        pytest.skip("Not applicable for asyncio")
+
+    reader, writer = await get_tcp_comm_pair()
+
+    with pytest.raises(asyncio.TimeoutError):
+        await asyncio.wait_for(reader.read(), 0.01)
+
+    assert reader.closed()
 
     await reader.close()
     await writer.close()