How does out of network get billed to the medical insurance policy holder?

Generally the provider will bill the insurance company just as an in-network provider will. Then the carrier will send an Explanation Of Benefits (EOB) to the policy holder just as they always do. What changes is how much they will pay and how much you will need to pay.

Let's say a procedure is billed at $300 and the in-network price (negotiated rate) is $100. You would pay whatever your potion of the $100 negotiated rate you are responsible for and the carrier pays the balance. Say the carrier pays 80%. They pay $80, you pay $20 and the remaining $200 is discounted away.

Out of network the carrier works on the same negotiated rate from their perspective but generally at a lower percentage, say 50%. So they would pay $50 and the remaining $250 is your to pay unless you can work out a discount directly with the provider.