Any example of a necessary nullable foreign key?

Question

Customers
 customer_id

Orders
 order_id
 customer_id fk

If I have two tables and define a foreign key on customer_id in the Orders table, by allow

Answer 1

No, nullable foreign keys are never necessary.

You can always normalize an optional 1-many relationship. Taking your example, you may have the following tables:

Customers: customer_id, ...
Orders: order_id, ...
OrdersCustomers: order_id, customer_id
  UNIQUE(order_id)

The two unique constraints make sure that one order can belong to only one customer, and never to the same customer twice.

Whether you should always normalize such a relationship is a different story. In some cases denormalization may lead to simpler implementations.