diff --git a/music21/stream/base.py b/music21/stream/base.py
index 121bcc0bf..a8f2a9bcf 100644
--- a/music21/stream/base.py
+++ b/music21/stream/base.py
@@ -2699,6 +2699,35 @@ def storeAtEnd(self, itemOrList, ignoreSort=False):
         # Streams cannot reside in end elements, thus do not update is flat
         self.coreElementsChanged(updateIsFlat=False)
 
+    def isAtEnd(self, element: base.Music21Object) -> bool:
+        '''
+        Return True if `element` is stored at the end of this Stream
+        (via :meth:`~music21.stream.base.Stream.storeAtEnd`).
+
+        >>> s = stream.Stream()
+        >>> n = note.Note('C')
+        >>> s.append(n)
+        >>> b = bar.Barline()
+        >>> s.storeAtEnd(b)
+        >>> s.isAtEnd(b)
+        True
+        >>> s.isAtEnd(n)
+        False
+
+        If the element is not in this Stream, :exc:`~music21.sites.SitesException`
+        is raised:
+
+        >>> s.isAtEnd(note.Note('E'))
+        Traceback (most recent call last):
+        music21.sites.SitesException: an entry for this object 0x... is not stored in stream
+            <music21.stream.Stream 0x...>
+
+        * New in v11.
+
+        AI-assisted.
+        '''
+        return self.elementOffset(element, returnSpecial=True) is OffsetSpecial.AT_END
+
     # --------------------------------------------------------------------------
     # all the following call either insert() or append()
 
@@ -9500,7 +9529,10 @@ def findNextElementNotCoincident(
             # is unsorted originally, this "looking ahead" could become O(n^2).
             originallySorted = useStream.isSorted
             rests_lacking_durations: list[note.Rest] = []
-            for i, e in enumerate(useStream._elements):
+            for i, e in enumerate(useStream.elements):
+                if useStream.isAtEnd(e):
+                    # Elements stored at the end carry no quantizable offset.
+                    continue
                 if processOffsets:
                     o = useStream.elementOffset(e)
                     sign = 1
diff --git a/music21/stream/tests.py b/music21/stream/tests.py
index 5f2835685..0686170f9 100644
--- a/music21/stream/tests.py
+++ b/music21/stream/tests.py
@@ -5063,6 +5063,52 @@ def testStoreAtEndFailures(self):
         with self.assertRaises(StreamException):
             s.storeAtEnd(b2)
 
+    def testIsAtEnd(self):
+        '''
+        https://github.com/cuthbertLab/music21/issues/1069
+
+        AI-assisted.
+        '''
+        s = Stream()
+        n = note.Note('C')
+        s.append(n)
+        b = bar.Barline()
+        s.storeAtEnd(b)
+        self.assertTrue(s.isAtEnd(b))
+        self.assertFalse(s.isAtEnd(n))
+
+        m = Measure()
+        nM = note.Note('D')
+        m.append(nM)
+        rb = bar.Barline('final')
+        m.storeAtEnd(rb)
+        self.assertTrue(m.isAtEnd(rb))
+        self.assertFalse(m.isAtEnd(nM))
+
+        outsider = note.Note('E')
+        with self.assertRaises(sites.SitesException):
+            s.isAtEnd(outsider)
+
+    def testQuantizeKeepsElementsStoredAtEnd(self):
+        '''
+        quantize() iterates .elements and skips elements stored at the end, so a
+        barline keeps its AT_END position instead of being given a real offset.
+
+        AI-assisted.
+        '''
+        s = Stream()
+        n = note.Note()
+        n.quarterLength = 0.26
+        s.repeatInsert(n, [0.1, 0.49, 0.9])
+        b = bar.Barline()
+        s.storeAtEnd(b)
+
+        q = s.quantize(processOffsets=True, processDurations=True, inPlace=False)
+
+        quantizedBarline = q._endElements[0]
+        self.assertTrue(q.isAtEnd(quantizedBarline))
+        self.assertEqual([q.elementOffset(e) for e in q._elements], [0.0, 0.5, 1.0])
+
     def testElementsHighestTimeB(self):
         '''
         Test adding elements at the highest time position