Library Stabilization Fund Act This bill provides funds for library services and technology. These funds may be used for maintaining and enhancing library operations and services, offering greater access to technology (e.g., purchasing and lending hotspots and other technology), and ensuring training and technical support for libraries. The amounts provided by the bill are designated as an emergency requirement pursuant to the Statutory Pay-As-You-Go Act of 2010 (PAYGO) and the Senate PAYGO rule.