Border Safety and Security Act of 2023 This bill requires the Department of Homeland Security (DHS) to suspend the entry of certain non-U.S. nationals ( aliens under federal law) during any period when DHS cannot detain such an individual or return the individual to a foreign country contiguous to the United States. Specifically, DHS must suspend the entry of non-U.S. nationals who (1) are unlawfully present, (2) arrive in the United States at a time or place other than as designated by DHS, or (3) do not possess valid entry documents. A state may sue DHS to enforce this requirement. The bill also authorizes DHS to suspend the entry of such non-U.S. nationals if DHS determines that such a suspension is necessary to achieve operational control over such a border. (Under current law, such non-U.S. nationals who arrive at the border 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.)