re: have you ever seen a fab bill a customer's customer directly?
Absolutely never.
A contract die sales agreement is usually negotiated within a set of standard terms, including an agreement to purchase a minimum amount over a specified time, providing a design which conforms to set process design rules, agreement to payment terms (net 30, net 60, etc), and agreement to dispute resolution terms. New customers/weak customers are usually required to provide part of the payment before the first wafer starts begin. There is also usually an agreement on how engineers from supplier and customer will interface throughout the production commitment. Lastly, there is usually a commitment from the contract supplier on guaranteed minimum yields (good die/wafer as determined at wafer sort).
Of course, this all depends on whether the customer actually has something from which to produce masks
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