When Twilio receives an Opt-out keyword from one of your users, it adds this phone number to a list of blocked numbers. Twilio checks this list before sending any future outgoing messages.
Is there a place to find this blocked number list in the Twilio console?
There is not. You must keep track of the opt-out list yourself. Twilio will forward the opt-out keywords to your application to handle this.
Twilio support for opt-out keywords (SMS STOP filtering)
Using Advanced Opt-out (Which require a messaging service)