The answer to your questions here, is it depends what you set up in those subscriptions. The group they are attached to is the group you specifiy in the subscription you set up, if you set it to do so. If you do, then it will downgrade if you have set it to do so. In the "benefits" section of the subscription you set up, you would set it to move users to whatever group you choose, and set it to reset if you wish for it to move them back afterwards.
https://invisioncommunity.com/4guides/suite-applications/commerce/products-purchases/selling-subscriptions-r308/