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Every state manages school fundig differently, and within states, it can vary, too. But in California, most districts are funded by the state, and the funding formula is based on attendence (and details about the student population). Some districts opt to get their funding directly from local property taxes which don't vary by attendance, but most districts get more funding by accepting the state funding and choose that instead.

If public school attendence goes down in such a system, the school districts (and therefore the schools) get less funding, but tax collection probably doesn't change. Instead there will be a surplus in the general fund. California has a lot of formulaic budget requirements, so if attendence dropped enough, it might derail the rest of the budget, but I'm not familiar with how close to the requirements the school budget tracks.