There is a distinction between ethical standards and legal standards of the practice of law. Violation of an ethical standard (like failing to communicate or misrepresenting matters to a client) is not in and of itself a basis for a legal malpractice claim -- there must be a breach of the standard of practice as well.
West Virginia (WV) Legal Malpractice Information Center
In many cases, a qualified legal malpractice attorney will offer to take your case on a contingency basis, meaning that at the outset of the case, you will sign a contingency fee contract which means that you will not have to pay any money up front. You will only pay when the professional negligence attorney obtains a recovery for you. At that time, you will reimburse your lawyer for costs and pay legal fees for representation.
The short answer is no, not all attorneys in West Virginia are required to carry liability insurance. Even well-qualified, experienced attorneys can make an error or one of their staff members can forget a deadline or make a mistake.