Do you have a global unsubscribe list
No global unsub list. That is your responsibility, as the account holder, to make sure none of your opted-in subscribers are on the Do Not Contact List.
You do have an unsubscribe list with all of your unsubscribed people from your account. This can be fund by clicking on Contacts from the top navigation bar and clicking All Unsubscribed. You can search for a number to see if they are on this list.
If a person has unsubscribed, they can reply with the word start to your texting number to re-subscribe.