Rehabilitation for Multiemployer Pensions Act of 2019 This bill establishes the Pension Rehabilitation Administration within the Department of the Treasury and a related trust fund to make loans to certain multiemployer defined benefit pension plans. To receive a loan, a plan must be (1) in critical and declining status, including any plan with respect to which a suspension of benefits has been approved; (2) in critical status, have a modified funded percentage of less than 40%, and have a ratio of active to inactive participants which is less than two to five; or (3) insolvent, if the plan became insolvent after December 16, 2014, and has not been terminated. Treasury must transfer amounts, which may include proceeds from bonds and other obligations, from the general fund to the trust fund established by this bill as necessary to fund the program. The Pension Rehabilitation Administration may use the funds, without a further appropriation, to make loans, pay principal and interest on obligations, or for administrative and operating expenses. The bill allows the sponsor of a multiemployer pension plan that is applying for a loan under this bill to also apply to the Pension Benefit Guaranty Corporation (PBGC) for financial assistance if, after receiving the loan, the plan will still become (or remain) insolvent within the 30-year period beginning on the date of the loan. The bill also appropriates to the PBGC the funds that are necessary to provide the financial assistance required by this bill. The bill modifies the requirements for the distribution of remaining pension benefits from certain defined contribution plans to a designated beneficiary upon death of an employee. The bill increases penalties for failure to file a tax return, and certain retirement plan returns.