There are various ways to unsubscribe/subscribe a contact from any list. It can be done from the contact's show up page as well as the API call:
A) Subscribe/Unsubscribe from the contact's show page, the below are the steps:-
1. Search for the contact from the Search widget on the Dashboard, it will take you to that Contact's Profile/Show page (this page shows the detailed information about the contact).
2. Once the page is opened, look for the list from which you want to unsubscribe/subscribe the contact, now click on "Toggle status" to change the subscription of the contact. Below is the screenshot.
The same process can be followed to Re-subscribe the contact in the list.
B) The same can also be accomplished from the PUT API call, contacts #update. You can change the Subscribe type value to false (unsubscribe) or true (subscribe) depending upon the requirement. Below is the screenshot.
Please replace the account id, list id, format, and the auth_token accordingly and make sure to pass the headers!
C) Also, it can be done by clicking on contacts under the list name and click on the subscription status of the contact. Below is the screenshot.