diff --git a/cloudpickle/cloudpickle.py b/cloudpickle/cloudpickle.py
index 030d44a3f..759cdb22a 100644
--- a/cloudpickle/cloudpickle.py
+++ b/cloudpickle/cloudpickle.py
@@ -492,8 +492,9 @@ def extract_func_data(self, func):
 
         # process closure
         closure = (
-            [c.cell_contents for c in func.__closure__]
-            if func.__closure__ is not None else None
+            list(map(_get_cell_contents, func.__closure__))
+            if func.__closure__ is not None
+            else None
         )
 
         # save the dict
@@ -896,6 +897,40 @@ def _gen_ellipsis():
 def _gen_not_implemented():
     return NotImplemented
 
+
+def _get_cell_contents(cell):
+    try:
+        return cell.cell_contents
+    except ValueError:
+        # sentinel used by ``_fill_function`` which will leave the cell empty
+        return _empty_cell_value
+
+
+def instance(cls):
+    """Create a new instance of a class.
+
+    Parameters
+    ----------
+    cls : type
+        The class to create an instance of.
+
+    Returns
+    -------
+    instance : cls
+        A new instance of ``cls``.
+    """
+    return cls()
+
+
+@instance
+class _empty_cell_value(object):
+    """sentinel for empty closures
+    """
+    @classmethod
+    def __reduce__(cls):
+        return cls.__name__
+
+
 def _fill_function(func, globals, defaults, dict, closure_values):
     """ Fills in the rest of function data into the skeleton function object
         that were created via _make_skel_func().
@@ -907,7 +942,8 @@ def _fill_function(func, globals, defaults, dict, closure_values):
     cells = func.__closure__
     if cells is not None:
         for cell, value in zip(cells, closure_values):
-            cell_set(cell, value)
+            if value is not _empty_cell_value:
+                cell_set(cell, value)
 
     return func
 
diff --git a/tests/cloudpickle_test.py b/tests/cloudpickle_test.py
index 19f1faf1f..f27cb7cba 100644
--- a/tests/cloudpickle_test.py
+++ b/tests/cloudpickle_test.py
@@ -167,6 +167,24 @@ def f():
             msg='g now has closure cells even though f does not',
         )
 
+    def test_empty_cell_preserved(self):
+        def f():
+            if False:  # pragma: no cover
+                cell = None
+
+            def g():
+                cell  # NameError, unbound free variable
+
+            return g
+
+        g1 = f()
+        with pytest.raises(NameError):
+            g1()
+
+        g2 = pickle_depickle(g1)
+        with pytest.raises(NameError):
+            g2()
+
     def test_unhashable_closure(self):
         def f():
             s = set((1, 2))  # mutable set is unhashable