Creates the Wage Insurance Act. Requires the Department of Employment Security to establish a Wage Insurance Program. Provides that an individual is eligible for wage insurance benefits if the individual is a claimant under the Unemployment Insurance Act at the time the individual obtains reemployment and is not employed by the employer from which the individual was last separated. Provides that benefits shall be paid in an amount sufficient to pay the difference between the wage received by the individual at the time of separation and the wages received by the individual from reemployment. Imposes a 0.4% payroll tax on employees beginning January 1, 2022. Provides that claims for wage insurance benefits may be filed beginning June 1, 2022. Contains provisions concerning the recovery of erroneous payments; hearings; civil penalties; unpaid taxes; rules; and other matters. Creates the Wage Insurance Fund as a special fund in the State treasury. Amends the State Finance Act to include the Wage Insurance Fund. Amends the Freedom of Information Act. Exempts from inspection and copying information that is exempt from disclosure under the Wage Insurance Act.