Protect Asylum Seekers Act This bill limits the separation of alien families and provides protections for asylum seekers. Certain civil and criminal penalties related to improper entry into the United States shall not apply if, after entering the United States, an alien without delay communicates to an immigration or asylum officer a non-fraudulent (1) desire to seek asylum, or (2) fear of persecution. The Departments of Homeland Security (DHS), Justice, and Health and Human Services shall not separate a child from a parent or legal guardian unless a state court terminates the parent or legal guardian's rights; a state child welfare agency or court determines it is in the child's best interests to be removed; or the child is determined to be a trafficking victim or at risk of becoming one, the accompanying adult is most likely not the parent or legal guardian, or the child is in danger of abuse or neglect. An agency may not separate a child from a parent or legal guardian solely to deter migration into the United States or to promote compliance with immigration laws. DHS shall develop (1) training related to the bill's family separation requirements, and (2) guidance for how parents and legal guardians may locate a separated child. DHS shall provide parents and legal guardians periodic status updates about a separated child. The Government Accountability Office shall report to Congress on the criminal prosecution of asylum seekers.