The relative voting power of the members does not apply when the judicial dissolution statute is used. The reason to ask a court to order dissolution is that the members themselves, or at least the member desiring dissolution, is unable to achieve dissolution through normal voting means. For example, in a 50/50 LLC in your example if the members agreed on dissolution then there would be no need to involve the court.
Judicial dissolution provides a court with a wide range of discretion to find a way to resolve serious intra-company disagreements. These discretionary methods first developed in corporate law, and over time courts started using creative methods to resolve the disputes without having to kill the company by dissolving it. Those same methods and policies have now been applied to limited liability companies. One of the methods developed was for a court to determine that dissolution was appropriate, but to give the company (and the other owners) an opportunity to buy the disgruntled member's ownership interest as an alternative to dissolving the company. The statute you mention is a formal authorization for a court to do precisely that.
Typically, you have to assert some legitimate grounds for obtaining dissolution. This could include fraud or wasting assets, but it may also include situations where it is not practicable to carry on the business of the LLC. If you are in a 50/50 LLC and are not able to agree on significant issues, that deadlock may under certain circumstances be enough for a court to order dissolution and alternatively offer the option in the statute for the company and other member to buy you out.
Keep in mind, too, that the "fair value" referred to does not necessarily mean fair market value, and there is a wide range of ways that value is determined. Courts differ greatly on what standards to apply. When you are ready to consider your next step, you should absolutely consult with an attorney who is licensed in North Carolina and who is familiar with how courts have interpreted this statute in previous cases.
I am answering general questions about legal situations to help you determine whether or not you should seek the advice of a licensed attorney in the state in which your legal issues arises. I have not been retained by you, nor am I your attorney unless we later enter into a formal, written agreement for you to engage me that we both sign. You are advised to seek formal legal counsel regarding your question.
I believe what this is stating is that if any remaining member(s) want to continue the business then they can acquire the interest from any member(s) that wish to remove themselves (those that complained to the court).
There is no deadlock here, if you want to dissolve but the other member would rather take your interest and continue the business then you both would be wise to work out an agreement now and avoid court. Otherwise, the court will allow the other member to buy your interest at FMV.
Probably a good idea to discuss in more detail with a lawyer before making a decision.
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