Dependent Care Expense Relief Act of 2020 This bill allows the carryover of unused dependent care flexible spending arrangement benefits from plan year 2020 to plan year 2021. It also allows employees terminated from employment to be reimbursed for unused dependent care benefits during a specified period. The bill requires the Department of the Treasury to issue rules or guidance to expand the definition of dependent care expenses eligible to be reimbursed from a dependent care flexible spending arrangement to account for changes in the dependent care needs of taxpayers due to a COVID-19 (i.e., corornavirus disease 2019) emergency declaration.