State and Local Government Cybersecurity Act of 2019 This bill provides for collaboration between the Department of Homeland Security (DHS) and state, local, tribal, and territorial governments, as well as corporations, associations, and the general public, regarding cybersecurity. The bill also provides for collaboration with foreign, as well as domestic, governmental agencies or entities, or corporations or associations. The bill expands DHS responsibilities through grants and cooperative agreements, including provision of assistance and education related to cyber threat indicators, defensive measures and cybersecurity technologies, cybersecurity risks, incidents, analysis, and warnings. The bill requires the National Cybersecurity and Communications Integration Center to coordinate with entities such as the Multi-State Information Sharing and Analysis Center to (1) conduct exercises, (2) provide operational and technical cybersecurity training, and (3) promote cybersecurity education and awareness. DHS may establish an initiative to enhance efforts to deploy technical or analytic capabilities or services that utilize classified cyber threat indicators or intelligence to detect or prevent malicious network traffic on unclassified non-federal information systems.