Opposite value for RESTRICT in foreign keys?

I apologize if this is a simple question, but after much searching
through google and the list archives, I cannot find any answer. My
question is this:

Say I have two tables:

CREATE TABLE products(
id int,
name varchar(50)
);

CREATE TABLE orders(
id int,
product_id int,
customer varchar(100)
FOREIGN KEY (product_id) REFERENCES products(id) ON UPDATE CASCADE ON
DELETE ???
);

Is there any way to create a foreign key that *allows* you to delete the
matching row from the referenced table (i.e. does the opposite of "NO
ACTION" or "RESTRICT")?

Basically, what I want to happen is:

* Whenever an order is created, the product_id field in the new record
MUST match an existing id field in the products table. (I don't want to
take orders for products that don't exist.)
* Whenver a product id is changed, all corresponding product_id's in the
orders table MUST be updated. (I want orders to match their respective
products even when the product's id is changed.)
* Whenever a product is deleted, all corresponding product_id's MUST NOT
be changed or deleted. (Even though the product is gone, I still want
the product_id to stay the same.)

As you can see I need referential integrity for every operation EXCEPT
deletion.

Is there any solution for this without scrapping the foreign key
altogether?

Thanks,

Brian Sanders
Webmaster
The Hotchkiss School
bsanders(at)hotchkiss(dot)org
860-435-3141