If you set the stock up so that when products_quantity hits <= 0 that the Product should be set to products_status 0 (removed from the Catalog) then this will work when Stock Tracking is turned on ...
However, existing Products that have products_quantity 0 will NOT be set to products_status 0 just because this switch is set, after the fact ...
The products_status is set during the checkout_process of the order ... and to adjust existing Products that have already gone to products_quantity <= 0 to be products_status 0 you need to do this either manually or you can issue a global update for this ...
NOTE: you can also set Products to show as Sold Out vs remove completely from the Catalog in the Stock settings as well ...
To globally update your Products to be products_status 0 when products_quantity is <= 0 you can run in the Tools ... Install SQL Patch ...
Code:
UPDATE products SET products_status = 0 WHERE products_quantity <= 0;