Emergency Unemployment Insurance Stabilization and Access Act of 2020 This bill responds to the coronavirus outbreak by expanding unemployment benefits and providing grants to states for processing and paying claims. Specifically, the bill requires the Department of Labor to transfer FY2020 emergency grants to a state's Unemployment Trust Fund to administer unemployment insurance. Grant recipients must (1) require employers to notify employees at the time they lose their jobs of the availability of unemployment compensation (UC), (2) ensure that UC applications and assistance with them are accessible, and (3) take certain steps to ensure the successful processing of applications. A state may receive an additional grant if its UC claims increased by 10% over the previous calendar year and it expresses its commitment to maintain and strengthen access to the UC system; and demonstrates steps to ease eligibility requirements and access to UC for claimants (e.g., waiving work search requirements and the waiting week, and relieving benefit charges for claimants and employers directly impacted by COVID-19 (i.e., coronavirus disease 2019) due to an illness in the workplace or direction from a public health official to isolate or quarantine workers). The bill (1) allows states to temporarily modify their UC laws and policies to respond to the spread of COVID-19; (2) waives interest on state loans for UC programs through December 31, 2020; (3) requires Labor to provide technical assistance and guidance to states for short-term UC programs; and (4) temporarily provides full federal financing of extended UC benefits, rather than requiring 50% state financing.