def METHOD_NAME(self) -> None:
    """Test that the background task to delete old device_inboxes works properly."""
    # create a valid device
    self.get_success(
        self.store.store_device(self.user_id, "cur_device", "display_name")
    )
    # Add device_inbox to devices
    self.get_success(
        self.store.db_pool.simple_insert(
            "device_inbox",
            {
                "user_id": self.user_id,
                "device_id": "cur_device",
                "stream_id": 1,
                "message_json": "{}",
            },
        )
    )
    self.get_success(
        self.store.db_pool.simple_insert(
            "device_inbox",
            {
                "user_id": self.user_id,
                "device_id": "old_device",
                "stream_id": 2,
                "message_json": "{}",
            },
        )
    )
    # Insert and run the background update.
    self.get_success(
        self.store.db_pool.simple_insert(
            "background_updates",
            {
                "update_name": "remove_dead_devices_from_device_inbox",
                "progress_json": "{}",
            },
        )
    )
    # ... and tell the DataStore that it hasn't finished all updates yet
    self.store.db_pool.updates._all_done = False
    self.wait_for_background_updates()
    # Make sure the background task deleted old device_inbox
    res = self.get_success(
        self.store.db_pool.simple_select_onecol(
            table="device_inbox",
            keyvalues={},
            retcol="device_id",
            desc="get_device_id_from_device_inbox",
        )
    )
    self.assertEqual(1, len(res))
    self.assertEqual(res[0], "cur_device")