diff --git a/openedx/core/djangoapps/content_libraries/api/blocks.py b/openedx/core/djangoapps/content_libraries/api/blocks.py
index 3678ea9f42d6..0400ede848de 100644
--- a/openedx/core/djangoapps/content_libraries/api/blocks.py
+++ b/openedx/core/djangoapps/content_libraries/api/blocks.py
@@ -385,10 +385,16 @@ def _import_staged_block(
     staged_content_id: int,
     staged_content_files: list[StagedContentFileData],
     now: datetime,
+    *,
+    can_stand_alone: bool = True,
 ) -> LibraryXBlockMetadata:
     """
     Create a new library block and populate it with staged content from clipboard
 
+    Set ``can_stand_alone=False`` when the block is being created as a child
+    of a container (e.g. a Unit being pasted from a course), so it is not
+    listed as a top-level library item. See bug #38132.
+
     Returns the newly created library block
     """
     from openedx.core.djangoapps.content_staging import api as content_staging_api
@@ -427,6 +433,7 @@ def _import_staged_block(
             local_key=usage_key.block_id,
             created=now,
             created_by=user.id,
+            can_stand_alone=can_stand_alone,
         )
 
         # This will create the first component version and set the OLX/title
@@ -602,7 +609,9 @@ def _import_staged_block_as_container(
             new_child_keys.append(child_container.container_key)
             continue
 
-        # This is not a container, so we import it as a standalone block
+        # This is not a container, so we import it as a child component.
+        # Mark it as can_stand_alone=False so it is owned by the Unit and
+        # does not leak into the top-level library listing. See bug #38132.
         try:
             if copied_from_block in copied_from_map:
                 # This block was already copied from the library, so we just link it to the container
@@ -618,6 +627,7 @@ def _import_staged_block_as_container(
                 staged_content_id=staged_content_id,
                 staged_content_files=staged_content_files,
                 now=now,
+                can_stand_alone=False,
             )
             if copied_from_block:
                 copied_from_map[copied_from_block] = child_metadata.usage_key
diff --git a/openedx/core/djangoapps/content_libraries/tests/test_course_to_library.py b/openedx/core/djangoapps/content_libraries/tests/test_course_to_library.py
index 7bc7da0fc868..c63d7158eae5 100644
--- a/openedx/core/djangoapps/content_libraries/tests/test_course_to_library.py
+++ b/openedx/core/djangoapps/content_libraries/tests/test_course_to_library.py
@@ -78,3 +78,47 @@ def test_library_paste_unit_from_course(self):
                 "block_type": "poll_question",
             })
             assert children[3]["id"].startswith("lb:CL-TEST:test_lib_paste_clipboard:poll_question:change-your-answer-")
+
+            # Regression for bug #38132: every child must be marked
+            # can_stand_alone=False so it is owned by the Unit and does not
+            # leak into the top-level library listing. Before the fix the
+            # default was True and children appeared as orphan top-level items
+            # that could not be deleted cleanly.
+            for child in children:
+                assert child.get("can_stand_alone") is False, (
+                    f"pasted child {child['id']} must have can_stand_alone=False"
+                )
+
+    def test_bug_38132_regression_pasted_unit_children_not_standalone(self):
+        """
+        Regression test for bug #38132: after pasting a Unit from a course
+        into a library, the unit's children must be marked can_stand_alone=False
+        so the top-level library listing does not contain orphan components
+        that cannot be deleted.
+        """
+        author = UserFactory.create(
+            username="Author38132",
+            email="author38132@example.com",
+            is_staff=True,
+        )
+        with self.as_user(author):
+            lib = self._create_library(
+                slug="test_lib_bug_38132",
+                title="Bug 38132 regression",
+                description="",
+            )
+            lib_id = lib["id"]
+
+            course_key = ToyCourseFactory.create().id
+            unit_key = course_key.make_usage_key("vertical", "vertical_test")
+            self._api(
+                'post',
+                "/api/content-staging/v1/clipboard/",
+                {"usage_key": str(unit_key)},
+                expect_response=200,
+            )
+            paste_data = self._paste_clipboard_content_in_library(lib_id)
+            children = self._get_container_children(paste_data["id"])
+            assert len(children) >= 1
+            for child in children:
+                assert child.get("can_stand_alone") is False