Housing Accountability Act of 2021 This bill provides statutory authority for the requirement that a property owner receiving low-income housing assistance payments for an existing public housing unit must maintain decent, safe, and sanitary conditions for the housing structure. The Department of Housing and Urban Development (HUD) must survey tenants of these structures semiannually to identify problems with the structures or with management. A structure must be referred to HUD for remediation if consistent or persistent problems are identified. HUD may impose penalties on an owner of a structure that violates this bill.