If something is unanswered, it gets no response, even when one is asked for or expected. So that unanswered text message? It hasn't gotten a reply.
An unanswered phone call isn't answered but instead just rings and rings endlessly. An unanswered question hovers there without a response, like when your dad asks, "Who's responsible for this mess?" and none of your siblings says a thing. If you write dozens of letters to your favorite Hollywood star but don't get a reply, those are (sadly) unanswered too.