Where is the savings going to come from as a result of the schools closing? Teachers are still being paid as are administrators. Or at least they are still working. Cafeteria staff are still preparing lunches for delivery. Obviously some things are "savings" - power, etc - but it won't be huge.
Yes, salary is probably 35-40% of all school district budgets but the operational costs of not opening the buildings are huge. Take out lunches are likely being done with the federal lunch money program (USDA grant I think or using up food that would spoil). Buses aren't running, no fuel costs, no maintenance costs. No supply costs in schools. They are probably saving at least 30% of budget.
If the federal government still funds as if the students are physically in the building, its going to be a boon.