Democracy Restoration Act of 2019 This bill addresses the voting rights of persons convicted of a criminal offense and the restoration of their voting rights. The bill declares that the right of a U.S. citizen to vote in any election for federal office shall not be denied or abridged because that individual has been convicted of a criminal offense unless, at the time of the election, such individual is serving a felony sentence. The bill provides for enforcement of, and remedies for violations of, the bill. The bill sets forth requirements for state and federal notification of individuals of the restoration of their voting rights. The bill prohibits federal funding of construction or improvement of a place of incarceration unless U.S. citizens incarcerated in that jurisdiction are notified, upon release, of their voting rights.