I don't know what you mean regarding pivot_root affecting file descriptors because they are not modified, they point to new names because the enclosing directory has been moved/renamed. There is a small race between moving items in the root directory as well as after moving all items and before starting pivot_root, but that race doesn't involve file descriptors but opening at the old paths before the new one is established, though lots of things use openat() these days so it doesn't really even occur in most cases then.