Protecting Benefits for Elderly Refugees and Refugees with Disabilities During COVID-19 Act of 2020 This bill extends the eligibility period for certain aliens to receive Supplemental Security Income (SSI) benefits. The bill also waives naturalization fees for SSI recipients. Currently, certain aliens, such as refugees and victims of trafficking, are eligible to receive SSI benefits for a seven-year period. For such an alien whose eligibility expired after January 31, 2020, this bill extends that alien's eligibility to September 30, 2021. Furthermore, during the period from January 31, 2020, to September 30, 2021, such a qualifying alien's eligibility for SSI benefits shall not expire while the alien has (1) a pending naturalization application, (2) an application on appeal, or (3) an accepted application but the alien has not yet sworn in as a U.S. citizen.