what happens
to the kids if the voucher money runs out in mid-year in the
private school? Are they allowed to show up on the public
school's doorstep, and demand to be educated?

Why not? They are still payig for public educations over & above any of the
proposed voucher amounts I've seen. The amounts are also much less than it
costs the local school system to "educate" that student. I have a friend who
home schools every other year to give his kids social skills. They are usually
half a year ahead when they go in to the publc shools. The family lives on @
12K a year.
Greg Sefton