Final answer:
The authority to appropriate funds to agencies experiencing a shortfall between legislative sessions typically lies with the Emergency Budget Committee.
Step-by-step explanation:
The authority to appropriate funds to agencies experiencing a shortfall between meetings of the legislature generally belongs to an entity that has the responsibility for overseeing the state's finances and budget. In most states, the governor initiates a budget proposal, indicating funding priorities and appropriating amounts to various state agencies. During times of fiscal distress or when the legislature is not in session, it is typically the governor or their finance director who has the discretion to adjust budgets. However, the legislature has the power of the purse and controls the appropriations process, allocating the government's money to various agencies. When immediate budgetary issues arise, some states empower a specific committee or official to manage shortfalls. Based on the information provided, the most likely answer would be the Emergency Budget Committee, whose role would be to address the financial issues that occur between legislative sessions.