Protecting Consumers from Unreasonable Rates Act of 2020 This bill requires the Department of Health and Human Services (HHS) or the relevant state agency to ensure that any excessive, unjustified, or unfairly discriminatory premium rates for health care coverage are corrected before, or as soon as possible after, implementation, including through mechanisms such as denying rates, modifying rates, or requiring rebates to consumers. HHS may apply civil monetary penalties to health insurers that fail to comply with a corrective action taken by HHS and may decertify the plan as a qualified health plan. (Qualified health plans are sold on health insurance exchanges, the only plans eligible for premium subsidies, and meet the requirements for minimum essential coverage.) HHS must determine whether HHS or the state will undertake the corrective actions based on whether the state can adequately undertake the actions. The bill declares that the review by HHS of unreasonable increases in premiums does not prohibit a state from imposing on health insurers additional rate requirements that are more protective of consumers. The HHS review, which currently covers only premium increases, is expanded to include all rate increases.