Text messages fall in to three different category statuses.
First is sent, which means that the text message has been sent and is still waiting on confirmation of delivery from the carrier.
Second is delivered, which means that the text message has been both sent from our end and received by the carrier.
Third is failed, Failed Messages can fall into a few categories. Either the phone number you are attempting to send has unsubscribed in the past from receiving messages, the carrier has filtered your message and chosen not to deliver it, or the number is not capable of receiving messages.
In the event that the carrier has filtered the message, that typically is done by an automatic trigger on their end.