From a pure economic standpoint, if you can't reduce fixed costs after the reduction of a student, that student did not contribute to fixed costs.
The term fixed cost can be used to describe short-term obligations (e.g. salaries, leases, etc.) and long-term capital expenses (e.g. bond repayments, etc.). Since a district's general fund does not include the capital costs associated with a building, and because the charter funding debate is always centered around a school district's general fund and operating expenses, I will only focus on short-term obligations.
In Ohio, a school board must approve its district's annual appropriation before the start of the next fiscal year (beginning July 1). The initial appropriation can be a temporary measure, with all districts having to approve a permanent appropriation measure by the 1st of October. Even though the permanent appropriation measure can be modified throughout the school year, the permanent appropriation measure reflects the likely general fund expenditures for the school year.
Each district in Ohio bases its budget on projected student enrollment (ADM). The process to estimate actual enrollment is difficult and subject to error. If a district miscalculates its ADM, it usually cannot make mid-year corrections since districts typically don't hire additional teachers or RIF excess teachers during the current school year. Districts can correct enrollment projection errors when approving the subsequent year's budget, but once set, a budget and its associated contracts create short-term fixed costs for the current school year.
What does the first sentence mean in light of what I've just discussed? It's simple, there are fixed costs based on the current budget, but those costs are short-term and may not even be associated with the student who transfers to a charter school.
Example: If an elementary has 600 students and one child moves in after the budget was set and subsequently transfers to a charter school, there is no way to reduce fixed costs since the current budget had been approved. Though costs cannot be reduced, state basic aid flows to the district and then out again, this time to the charter where the child has enrolled. 
In order to understand the impact of this transfer, one has to go back in time to the point where that child entered the school. Upon enrollment, overhead costs were already fixed so the school did not incur additional fixed costs due to that child. Therefore, at the margin, no fixed cost can be attributed to that child, whether on the way in or way out of the school. This child was expenditure neutral.
Fixed costs can be attributed to the student whose enrollment brings about a new section, school, etc. If a district loses enough students that it can reduce staff or close an elementary, the fixed costs associated with the section or school are wiped from the books.
If a student causes the need for a new third grade section, the marginal fixed cost associated with the child are the costs of operating an additional section; new teacher contract, etc. Subsequent third grade students result in no additional fixed costs and only minimal operating costs since the section is already available with empty seats. If the subsequent students transfer to a charter school, no fixed costs can be reduced since no fixed costs were incurred due to their enrollment. When the child that caused the opening of the new section transfers, the fixed costs associated with the child are wiped from the books since the section, and teaching position, etc., are no longer needed.
In Ohio, if a district opens its doors to more students than planned, it sees a revenue gain. The district's operating costs were fixed by the budget, so each new student provides approximately $5,400 in additional state funding aid while only creating small additional operating costs; for water, paper, etc. Low estimates create a financial bonus.
High estimates, conversely, create financial distress. In such situation, costs were fixed by the budget yet the district loses approximately $5,400 for each student that doesn't arrive as planned.
But these hardships are not the result of charter schools; they are purely the result of poor planning by the district. Student populations change over time as students move into and out of districts, change to and from private schools, and choose or return from home schooling. None of these other movements of students are criticized like charter school enrollment, but there is no real difference between them; all cause an increase or decrease of $5,400 for each student over or under enrollment projections.
In fact, some of these movements are cheered. Districts encourage their students to enroll in colleges and universities through post secondary options enrollment, as well as encourage students to attend alternative schools such as the Columbus Zoo's Zoo School. Each of these activities cause funds to leave the district, yet there are few critics of such alternative programs.
Part of the confusion comes from the presentation of state basic aid on the Ohio Department of Educations SF3 form. The forms leaves the impression that the state funds on a per student basis at the state share percentage . In addition, districts also believe that fixed overhead costs are apportioned out to students equally. These are absolutely not the case.
The confusion is also due to districts not understanding the effects of changes over time. In the year after an outflow to charters or other situations, districts can reduce administration and staff to recoup most of the fixed costs. That said, some costs, such as the need for a board of education, superintendent, treasurer, and at least one teacher, educational service personnel, etc., are truly fixed but are nothing compared to property tax revenue being generated locally.
Word for the wise: Revenue and costs function at the margin, never at the average.