@@ -20,6 +20,9 @@
 
 _log = logging.getLogger(__name__)
 
+# a tombstone sentinel to ensure we never reset the axes or figure on an Artist
+_tombstone = object()
+
 
 def _prevent_rasterization(draw):
     # We assume that by default artists are not allowed to rasterize (unless
@@ -181,7 +184,7 @@ def __init__(self):
         self._stale = True
         self.stale_callback = None
         self._axes = None
-        self.figure = None
+        self._figure = None
 
         self._transform = None
         self._transformSet = False
@@ -293,18 +296,60 @@ def convert_yunits(self, y):
     @property
     def axes(self):
         """The `~.axes.Axes` instance the artist resides in, or *None*."""
-        return self._axes
+        return self._axes if self._axes is not _tombstone else None
 
     @axes.setter
     def axes(self, new_axes):
         if (new_axes is not None and self._axes is not None
                 and new_axes != self._axes):
-            raise ValueError("Can not reset the Axes. You are probably trying to reuse "
-                             "an artist in more than one Axes which is not supported")
+            if self._axes is _tombstone:
+                extra = (
+                    f"The artist {self!r} has had its Axes reset to None " +
+                    "but was previously included in one."
+                )
+            else:
+                extra = (
+                    f"The artist {self!r} is currently in {self._axes!r} " +
+                    f"in the figure {self._axes.figure!r}."
+                )
+            raise ValueError("Can not reset the Axes.  You are probably " +
+                             "trying to re-use an artist in more than one " +
+                             "Axes which is not supported.  " +
+                             extra
+                             )
+        if self._axes is not None and new_axes is None:
+            new_axes = _tombstone
         self._axes = new_axes
         if new_axes is not None and new_axes is not self:
             self.stale_callback = _stale_axes_callback
 
+    @property
+    def figure(self):
+        """The `~.figure.Figure` instance the artist resides in, or *None*."""
+        return self._figure if self._figure is not _tombstone else None
+
+    @figure.setter
+    def figure(self, new_figure):
+        if (new_figure is not None and self._figure is not None
+                and new_figure != self._figure and new_figure is not True):
+            if self._figure is _tombstone:
+                extra = (
+                    f"The artist {self!r} has had its Figure reset to None " +
+                    "but was previously included in one."
+                )
+            else:
+                extra = (
+                    f"The artist {self!r} is currently in {self._figure!r}."
+                )
+            raise ValueError("Can not reset the figure.  You are probably " +
+                             "trying to re-use an artist in more than one " +
+                             "Figure which is not supported.  " +
+                             extra
+                             )
+        if self._figure is not None and new_figure is None:
+            new_figure = _tombstone
+        self._figure = new_figure
+
     @property
     def stale(self):
         """
@@ -738,14 +783,6 @@ def set_figure(self, fig):
         # if this is a no-op just return
         if self.figure is fig:
             return
-        # if we currently have a figure (the case of both `self.figure`
-        # and *fig* being none is taken care of above) we then user is
-        # trying to change the figure an artist is associated with which
-        # is not allowed for the same reason as adding the same instance
-        # to more than one Axes
-        if self.figure is not None:
-            raise RuntimeError("Can not put single artist in "
-                               "more than one figure")
         self.figure = fig
         if self.figure and self.figure is not self:
             self.pchanged()
 
@@ -137,6 +137,7 @@ def __init__(self, **kwargs):
         # axis._get_tick_boxes_siblings
         self._align_label_groups = {"x": cbook.Grouper(), "y": cbook.Grouper()}
 
+        self._figure = self
         self._localaxes = []  # track all Axes
         self.artists = []
         self.lines = []
@@ -2162,7 +2163,7 @@ def __init__(self, parent, subplotspec, *,
 
         self._subplotspec = subplotspec
         self._parent = parent
-        self.figure = parent.figure
+        self._figure = parent.figure
 
         # subfigures use the parent axstack
         self._axstack = parent._axstack
 
@@ -562,3 +562,36 @@ def draw(self, renderer, extra):
 
     assert 'aardvark' == art.draw(renderer, 'aardvark')
     assert 'aardvark' == art.draw(renderer, extra='aardvark')
+
+
+def test_no_reset():
+    fig, (ax1, ax2) = plt.subplots(2)
+    fig2 = plt.figure()
+    ln, = ax1.plot(range(5))
+    with pytest.raises(
+            ValueError, match=f"The artist {ln!r} is currently in {ax1!r}"
+    ):
+        ax2.add_line(ln)
+    with pytest.raises(
+            ValueError, match=f"The artist {ln!r} is currently in {ax1!r}"
+    ):
+        ln.axes = ax2
+    with pytest.raises(
+            ValueError, match=f"The artist {ln!r} is currently in {fig!r}"
+    ):
+        ln.figure = fig2
+
+    ln.remove()
+    assert ln.figure is None
+    assert ln.axes is None
+    with pytest.raises(
+            ValueError, match=f"The artist {ln!r} has had its Figure reset "
+    ):
+        ax2.add_line(ln)
+    with pytest.raises(
+            ValueError, match=f"The artist {ln!r} has had its Axes reset "
+    ):
+        ln.axes = ax2
+
+    assert ln.axes is None
+    assert ln.figure is None