Economic Ladders to End Volatility and Advance Training and Employment Act of 2019 or the ELEVATE Act of 2019 This bill establishes a federal program to help fund (1) state- and tribe-run job-assistance programs, and (2) assistance for self-employed individuals and workers who relocate for employment opportunities. The Department of Health and Human Services shall provide funds for programs that assist eligible individuals, such as those who face barriers to employment. Such programs shall provide employment services, training, and related services. The bill also establishes criteria for using such funds for various purposes, including subsidized jobs. The bill also establishes various reporting and application requirements for states seeking funds for such programs. The bill establishes an assistance program for self-employed individuals who meet various requirements and whose most recent contracts ended through no fault of their own. Such individuals shall be entitled to a weekly benefit equal to half of the average weekly earnings from their last employment, not to exceed the maximum available for unemployment benefits. An individual may not concurrently receive unemployment compensation and self-employment assistance. Dislocated workers and long-term unemployed individuals shall be entitled to assistance for moving to a new area to earn family-sustaining employment. Such assistance may cover up to 90% of reasonable expenses, subject to a cap of $2,000 for an individual. The bill establishes the Office of Reemployment Assistance in the Social Security Administration to administer the self-employment and relocation assistance programs.