The current federal law has a requirement that a student in a low performing school may transfer to another school within the school system where that student is enrolled. Students may not transfer to another school system.
Essentially this means that a child can attend any school, regardless of location or family income. There are different types though such as:
Vouchers: This is a certificate issued by the government by which PARENTS CAN PAY for their child at another school instead of them attending the school assigned to them.
There are scholarship programs: People/companies can get a tax credit for donations that you may use to send your child to another school.
Personal tax credits & deductions: You can receive a tax deduction for approved educational expenses that you may have from a private school.
The link below will provide more information, but basically to answer your question NO it will not be paid for by the failing district and this seems so unfair because you are still paying taxes in your community and to give your child a better education, must endure other expenses as well. I've also included a link to a story about a woman who has been placed in jail over such an issue. It's a sad, but interesting story.