diff --git a/src/auditwheel/elfutils.py b/src/auditwheel/elfutils.py
index f375a20c..677fe169 100644
--- a/src/auditwheel/elfutils.py
+++ b/src/auditwheel/elfutils.py
@@ -117,9 +117,19 @@ def elf_read_rpaths(fn: Path) -> dict[str, list[str]]:
 
         for t in section.iter_tags():
             if t.entry.d_tag == "DT_RPATH":
-                result["rpaths"] = parse_ld_paths(t.rpath, root="/", path=str(fn))
+                result["rpaths"] = parse_ld_paths(
+                    t.rpath,
+                    root="/",
+                    path=str(fn),
+                    keep_non_exist=True,
+                )
             elif t.entry.d_tag == "DT_RUNPATH":
-                result["runpaths"] = parse_ld_paths(t.runpath, root="/", path=str(fn))
+                result["runpaths"] = parse_ld_paths(
+                    t.runpath,
+                    root="/",
+                    path=str(fn),
+                    keep_non_exist=True,
+                )
 
     return result
 
diff --git a/src/auditwheel/lddtree.py b/src/auditwheel/lddtree.py
index 76fe6836..421bd35b 100644
--- a/src/auditwheel/lddtree.py
+++ b/src/auditwheel/lddtree.py
@@ -213,7 +213,12 @@ def dedupe(items: list[str]) -> list[str]:
     return [seen.setdefault(x, x) for x in items if x not in seen]
 
 
-def parse_ld_paths(str_ldpaths: str, path: str, root: str = "") -> list[str]:
+def parse_ld_paths(
+    str_ldpaths: str,
+    path: str,
+    root: str = "",
+    keep_non_exist: bool = False,  # noqa: FBT001, FBT002
+) -> list[str]:
     """Parse the colon-delimited list of paths and apply ldso rules to each
 
     Note the special handling as dictated by the ldso:
@@ -229,6 +234,8 @@ def parse_ld_paths(str_ldpaths: str, path: str, root: str = "") -> list[str]:
         The path to prepend to all paths found
     path
         The object actively being parsed (used for $ORIGIN)
+    keep_non_exist
+        Do not eliminate non-exist rpath from result
 
     Returns
     -------
@@ -245,7 +252,7 @@ def parse_ld_paths(str_ldpaths: str, path: str, root: str = "") -> list[str]:
         else:
             ldpath_ = root + ldpath
         ldpaths.append(normpath(ldpath_))
-    return [p for p in dedupe(ldpaths) if os.path.isdir(p)]
+    return [p for p in dedupe(ldpaths) if keep_non_exist or os.path.isdir(p)]
 
 
 @functools.lru_cache
diff --git a/tests/unit/test_repair.py b/tests/unit/test_repair.py
index 2a0df9d4..bfef1112 100644
--- a/tests/unit/test_repair.py
+++ b/tests/unit/test_repair.py
@@ -4,7 +4,7 @@
 from unittest.mock import call, patch
 
 from auditwheel.patcher import Patchelf
-from auditwheel.repair import append_rpath_within_wheel
+from auditwheel.repair import append_rpath_within_wheel, copylib
 
 
 @patch("auditwheel.patcher._verify_patchelf")
@@ -115,3 +115,27 @@ def test_append_rpath_ignore_relative(self, check_call, check_output, _):  # noq
 
         assert check_output.call_args_list == check_output_expected_args
         assert check_call.call_args_list == check_call_expected_args
+
+
+@patch("auditwheel.patcher._verify_patchelf")
+@patch("auditwheel.patcher.check_output")
+@patch("auditwheel.patcher.check_call")
+class TestCopylib:
+    @patch("auditwheel.repair.elf_read_rpaths")
+    def test_nonexistent_rpath(self, elf_read_rpaths, check_call, _0, _1, tmp_path):  # noqa: PT019
+        # When a library has a non-existent runpath, copylib should still
+        # call set_rpath to replace it with $ORIGIN
+        patcher = Patchelf()
+        src_path = tmp_path / "b.so"
+        src_path.write_bytes(b"\x00")
+        dest_dir = tmp_path / "dest"
+        dest_dir.mkdir()
+        elf_read_rpaths.return_value = {"rpaths": [], "runpaths": ["/nonexistent/path"]}
+
+        copylib(src_path, dest_dir, patcher)
+
+        elf_read_rpaths.assert_called_once_with(src_path)
+        dest_path = next(dest_dir.iterdir())
+        check_call.assert_any_call(
+            ["patchelf", "--force-rpath", "--set-rpath", "$ORIGIN", dest_path],
+        )