Solidarity in Salary Act of 2019 This bill provides for withholding or eliminating the pay of Members of Congress, the President, and the Vice President during a government shutdown. For the 116th Congress, the bill requires the salaries of Members of Congress to be held in escrow during a government shutdown and to be released on the earlier of (1) the date on which the government shutdown ends, or (2) the last day of the Congress. Beginning with the 117th Congress, the bill prohibits Members of Congress from being paid for the period of a government shutdown. The bill also requires the salaries of the President and the Vice President to be held in escrow during a government shutdown and to be released on the earlier of (1) the date on which the government shutdown ends, or (2) the last day of the term of office of the President and Vice President during which the government shutdown begins.