The Constitution does not allow for anyone who is not a natural-born citizen to become Acting President, even in this scenario. So Elaine Chao would still not become Acting President.
Neither the Constitution nor the United States Code specify what would happen if the entire line of succession is exhausted. This is why everything possible is done (notably having a designated survivor for events such as the State of the Union) to prevent it from happening. Some recommendations have been made on how to fill this gap, but as of this writing, none have been implemented.