diff --git a/src/anyio/_core/_sockets.py b/src/anyio/_core/_sockets.py
index 647597b6..388a869b 100644
--- a/src/anyio/_core/_sockets.py
+++ b/src/anyio/_core/_sockets.py
@@ -671,8 +671,12 @@ async def setup_unix_local_socket(
     if path is not None:
         path_str = str(path)
         path = Path(path)
-        if path.is_socket():
-            path.unlink()
+        if path_str.startswith("\0"):
+            # Unix abstract namespace socket. No file backing so skip stat call
+            pass
+        else:
+            if path.is_socket():
+                path.unlink()
     else:
         path_str = None
 
diff --git a/tests/test_sockets.py b/tests/test_sockets.py
index acffe920..cfbc496d 100644
--- a/tests/test_sockets.py
+++ b/tests/test_sockets.py
@@ -695,9 +695,16 @@ async def handle(stream: SocketStream) -> None:
     sys.platform == "win32", reason="UNIX sockets are not available on Windows"
 )
 class TestUNIXStream:
-    @pytest.fixture
-    def socket_path(self, tmp_path_factory: TempPathFactory) -> Path:
-        return tmp_path_factory.mktemp("unix").joinpath("socket")
+    @pytest.fixture(params=["path", "abstract"])
+    def socket_path(
+        self, request: SubRequest, tmp_path_factory: TempPathFactory
+    ) -> Path:
+        path = tmp_path_factory.mktemp("unix").joinpath("socket")
+
+        if request.param == "path":
+            return path
+        elif request.param == "abstract":
+            return Path(f"\0{path}")
 
     @pytest.fixture(params=[False, True], ids=["str", "path"])
     def socket_path_or_str(self, request: SubRequest, socket_path: Path) -> Path | str:
@@ -721,7 +728,15 @@ async def test_extra_attributes(
             assert (
                 stream.extra(SocketAttribute.local_address) == raw_socket.getsockname()
             )
-            assert stream.extra(SocketAttribute.remote_address) == str(socket_path)
+            remote_addr = stream.extra(SocketAttribute.remote_address)
+            if isinstance(remote_addr, str):
+                assert stream.extra(SocketAttribute.remote_address) == str(socket_path)
+            else:
+                assert isinstance(remote_addr, bytes)
+                assert stream.extra(SocketAttribute.remote_address) == bytes(
+                    socket_path
+                )
+
             pytest.raises(
                 TypedAttributeLookupError, stream.extra, SocketAttribute.local_port
             )
@@ -960,17 +975,28 @@ async def test_send_after_close(
             await stream.send(b"foo")
 
     async def test_cannot_connect(self, socket_path: Path) -> None:
-        with pytest.raises(FileNotFoundError):
-            await connect_unix(socket_path)
+        if str(socket_path).startswith("\0"):
+            with pytest.raises(ConnectionRefusedError):
+                await connect_unix(socket_path)
+        else:
+            with pytest.raises(FileNotFoundError):
+                await connect_unix(socket_path)
 
 
 @pytest.mark.skipif(
     sys.platform == "win32", reason="UNIX sockets are not available on Windows"
 )
 class TestUNIXListener:
-    @pytest.fixture
-    def socket_path(self, tmp_path_factory: TempPathFactory) -> Path:
-        return tmp_path_factory.mktemp("unix").joinpath("socket")
+    @pytest.fixture(params=["path", "abstract"])
+    def socket_path(
+        self, request: SubRequest, tmp_path_factory: TempPathFactory
+    ) -> Path:
+        path = tmp_path_factory.mktemp("unix").joinpath("socket")
+
+        if request.param == "path":
+            return path
+        elif request.param == "abstract":
+            return Path(f"\0{path}")
 
     @pytest.fixture(params=[False, True], ids=["str", "path"])
     def socket_path_or_str(self, request: SubRequest, socket_path: Path) -> Path | str: