Big Business 13 adds a setting for BigCommerce to ignore Orders but continue to automatically process inventory updates.
Normally you just choose the Status of Orders you want to import, such as Awaiting Fulfillment. Then Big Business finds new orders as soon at they come in.
Now you can choose Don't Get/Set/Use to skip orders but still use automation to Update Availability, for example.
In the picture, Get Orders With Status is set to Don't Get/Set/Use, so orders will be skipped. However, Update Availability is set to Qty Available, so when you sell inventory yourself, your online store is still updated so it knows what you have available to sell.