When last product is sold, does the product stay in Product database?

This must be a very basic thing but I ask it anyway..

When last product is sold, does the product stay in database so it can be activated again when new stock arrives again to physical shop?

So we do not have to make that product again with all the images, measures and prizes.

What about multisite? These products are not multisite-wide in WP Product administation, so all sites cannot see others off-line products. No, it cant be..

Only Global Product Categories are multisite-wide on frontend.
So each site administrator in multisite must create the product by themself for the first time, they can´t "copy" already created products from other sites in multisite. Right?

Pekka