Border Safety and Security Act of 2023 This bill requires the Department of Homeland Security (DHS) to suspend the entry of any non-U.S. nationals ( aliens under federal law) without valid entry documents during any period when DHS cannot detain such an individual or return the individual to a foreign country contiguous to the United States. A state may sue DHS to enforce this requirement. (Under current law, non-U.S. nationals who arrive at the border without entry documents are generally subject to expedited removal. However, if such an individual is found to have a credible fear of persecution, they are typically subject to detention while their asylum claim is being considered.) The bill also authorizes DHS to suspend the entry of non-U.S. nationals without entry documents at the border if DHS determines that such a suspension is necessary to achieve operational control over such a border.