The second case seems highly unlikely. A school would have to be very wealthy indeed to survive if it were to reject its prevailing source of regular income, the government. A school which had grown dependent on the program could be dealt a mortal blow if it withdrew or was expelled from the program. Good schools will not die out. There is more to the plight of the private school than the ability of the user to pay.
Willingness is a major factor.
A return to the first principles of their founders may not save private schools. But it is a first step, and a giant one, in the right direction. The voucher system is a step backward and downward into the mire of government control of all aspects of our lives. The man who is truly interested in quality education will look first to principles of freedom and honor. He may check the government schools to see if education based on compulsion in attendance and support can truly inculcate these principles.