Emergency Homelessness Assistance Act of 2021 This bill provides additional FY2021 funding for the Department of Housing and Urban Development's HOME Investment Partnerships Program. Funding is provided for tenant-based rental assistance, development and support of affordable housing, supportive housing services, and the acquisition of non-congregate shelter units. These units may remain non-congregate shelter units, be converted into permanent affordable housing, or be used as emergency shelter. Individuals qualifying for such assistance include at-risk veterans and individuals who are homeless, at risk of homelessness, or fleeing or attempting to flee domestic violence or other dangerous situations.