Public school funding is based on WADA ... or Weighted Average Daily Attendance. They get money based on a student butt in a seat on a given day. The basic allotment is based on the kid's butt being in the seat 100% of the days the school is open. Or ... on a school field trip or whatever. Being counted present for the day.
So, if a kid lives in the Del Valle ISD but transfers to Austin ISD, Austin ISD gets the $6500 for that kid.
If a kid lives in Austin ISD but is enrolled in Regents, a private school, Austin ISD gets $0 for that kid.
The public school does not "keep" the allotment because the allotment was never made, because the private school kid is not enrolled in the district.
If a kid lives in Austin ISD and attends Austin ISD, but the parents decide to pull the kid out of school for a week for a ski trip, the school gets $0 basic allotment funding for that kid for the days missed. The school still has expenses, lights, A/C, pay the teacher, pay the bus driver, provide the bus, they just don't have basic allotment funding for that kid for those days.
If the Regents kid get a new school voucher, they have $10,000 they can spend at Regents. It does not affect Austin ISD's funding. Regents charges $21,000 per year in tuition. Regents can choose to discount tuition for that kid because they are bringing a $10,000 voucher to the school, or they can keep tuition right where it is and suddenly Regents has an additional $10,000. I have not heard of a WADA component for the vouchers, so it's possible that this is $10,000 per year, even if the kid misses school for a week.