Not sure if this is a bug, or I am missing something but the unpublish feature of manage stock does not seem to work.
Example:
I have a T-shirt product with 2 variants, Red and White. I have 2 Red and 2 White shirts with a minimum stock of 1. The product is published as are both variants. Everything displays as expected.
If I change the Red variant to a stock of '0', set the 'Low Stock Activity' to 'unpublish', and click save the Red Variant is still visible on the T-shirt page.
Think I understand your query and this is by design rather than a bug.
If your stock reaches your low stock threshold as part of a purchase then the product variant will be unpublished. However, just setting the product stock to less than your stock threshold in administration will not automatically unpublish.
Reason for this is if you are setting stock level manually, you may as well unpublish manually at the same time.