Yes. That happened to a guy I knew. His ex got on line and set up an account through his mobile phone provider. She was reading our text messages. No wonder I seldom saw him. Every time he and I made plans, she suddenly couldn't pick-up the kids or whatever. Yes, absolutely people can do that. She was reading our messages live, on line. It is against the law but he was not willing to prosecute her. I am still mad about it. Maybe I should file a police report about her violating my privacy.
It is possible for some people to tap into your text messages through the use of a computer program or app. There are professional hackers who can gain access to your personal messages using very little details/information.