If a customer is subscribed to multiple SMS lists on Tatango, and they respond with the word "STOP" to unsubscribe, Tatango will unsubscribe that customer from the list in which they received the most recent message from. If a customer wishes to unsubscribe from all lists they are subscribed to, they can respond "STOP ALL".
For example, if your customer is subscribed to List A & B, and they respond to a message from list B with "STOP", Tatango will opt them out of List B, while the customer will remain a subscriber of List A.
Additional Notes
This applies for transactional messaging as well.