Here is some info from Twilio which should provide further insight into this topic:
Twilio support for opt-out keywords (SMS STOP filtering)
Twilio, by default, handles standard English-language reply messages such as STOP, UNSTOP, UNSUBSCRIBE or CANCEL for Toll-Free and Long Code messages, in accordance with industry standards. Supported opt-out and opt-in keywords for Twilio Programmable Messaging are listed below.
STOP, STOPALL, UNSUBSCRIBE, CANCEL, END, or QUIT
Any of these STOP keyword replies will prevent a customer from receiving new messages from the Twilio phone number they're responding to. When Twilio receives one of these replies, we will create a "blacklist" entry on our side, and then pass the message on to your webhook. Once we have a blacklist entry for a particular recipient phone number, any future attempts to message them will be met with a 400 response from our API, along with Error Code 21610 - Message cannot be sent to the 'To' number because the customer has replied with STOP. Recipients can disable this message stop, and resume receiving messages with the START, YES, or UNSTOP commands as outlined below.
Only single-word messages will trigger the block. So, for example, replying STOP will stop the customer from receiving messages from that particular Twilio number, but replying "STOP PLEASE" or "PLEASE CANCEL" will not. Further, the block works and is logged even if your number currently has no messaging request URL.
Please note that these STOP keyword replies only apply to the most recent number that messaged the recipient. If you are using more than one Toll-Free number or Long Code for sending messages, you must take additional action separate from Twilio to prevent these customers from receiving messages from your other numbers. We recommend "blacklisting" numbers on your side when one of these message responses is received at your webhook.
START, YES and UNSTOP
Any of these replies will opt customers back in to the messages coming from a Twilio Long Code. These messages will also be delivered to your Twilio account, and the defined web hook, so you can update your application logic.
Please note that Toll Free numbers only respond to UNSTOP.