Preventing Destabilization of Iraq Act of 2019 This bill directs the President to impose sanctions on foreign persons that use violence to threaten peace and stability in Iraq or to undermine the country's democratic processes and economic reconstruction. The sanctions include blocking property transactions involving such a sanctioned individual and blocking such a person's entry into the United States. Any current visas belonging to a sanctioned individual shall be revoked. The Department of State shall report to Congress whether certain groups, including Asa'ib Ahl al-Haq and Harakat Hizballah al-Nujaba, qualify as foreign terrorist organizations and whether such groups and individuals affiliated with such groups should be subject to various sanctions. The State Department shall also report to Congress whether certain individuals, including Qais al-Khazali and Laith al-Khazali, would be subject to the sanctions prescribed in this bill.