Yes, it's correct to keep those questions on the "unanswered" tab. The tab is not only for questions with no answers, but also for questions with no quality answers — no answers that have gotten any votes. Questions are in that state not just because of the asker, but also because nobody has read those answers and thought they were good enough to vote on.
You can think of the tab as a list of questions where there's an opportunity for someone (maybe you) to provide a better answer. There are lots of things you can do about a question on that list:
- If you think some of the existing answers are good, then vote them up. That will take the question off the "unanswered" list.
- If none of the answers are good enough to get your vote, but some are almost good, then edit to improve them, and then vote them up.
- If there are no answers, or none of the answers are close, then answer the question yourself. (That won't immediately take the question off the list, but it will promote the question to the front page, so new people might look, read your answer, and vote it up.)
- If the question isn't clear, post a comment asking for clarification.
- If you want to know the answer to the question, you can offer a bounty.
- If you don't know the answer, but you know someone else who might, then share the question with your friends and colleagues.
Another possibility is that the question doesn't really belong. In that case, vote to close it.