Safeguarding Election Infrastructure Act of 2019 This bill addresses the security of federal elections, including by requiring paper ballots, requiring audits of election results, and providing support for voting system security improvements. Voting systems must use individual, durable, voter-verified, paper ballots beginning one year after enactment of this bill. The ballots must be marked and made available for inspection and verification by the voter before the vote is cast and counted. The bill prohibits states or other jurisdictions from acquiring electronic voting systems for use in a federal election that do not produce a voter-verified paper record. States must audit election results in competitive races beginning in November 2022. Audits must consist of random hand counts of paper ballots. The Election Assistance Commission (EAC) must pay states to cover the costs of audits. The EAC must award grants to states to improve voting system security by updating or testing voting equipment, keeping offline backups of voter registration lists, providing a secure platform for disseminating vote totals, or taking other specified actions. If the Department of Homeland Security (DHS) determines that the security of a state's voting system or voter registration database was breached or is investigating whether a breach occurred, then DHS must report on the determination or investigation to specified congressional committees and the state election office. At the request of a state, DHS must collaborate with the state election office to help prevent and respond to threats to the security of the state's voting systems and voter registration databases.