Subject Re: [firebird-support] Comparing two tables and locate not matched question
Not sure from your question which table should be first, but wouldn't something like this work for you if
either Active_Inventory.product_ID was a Primary Key or both tables have a unique index on this field?

SELECT a.product_ID, b.product_ID 
FROM Active_Inventory a 
LEFT JOIN Vendor_Products b ON a.product_ID = b.product_ID
WHERE b.product_ID IS NULL