Limited liability companies are created with state law, and therefore they, and the rights of their owners, are governed by state law. A definitive answer to this question will depend on your state and its particular business laws.
As a general matter, most states will allow a member of an LLC to seek a dissolution of an LLC if there are opposing interests between the members. However, if the members cannot work it out between themselves, the court will have to get involved. It will take legal action and a court order to do so. If you find yourself approaching a legal dispute with your current or former business partner over the dissolution, you should consult with an experienced business attorney as soon as possible. Note that you’ll need to meet whatever standard your state’s laws set for allowing dissolution.
Obviously, if at all possible, you would prefer to do this without having to go to court. Once you bring a legal action, the time it takes for dissolution and the expense will both increase greatly. Therefore, you should try to come to a resolution or agreement with your partner (the other LLC member). Some factors to consider include:
Note that in terms of buying out each other’s interest, if the company has debts, one way to buy out the other member is to simply agree to take over or assume all of the debts or obligations, allowing the other person off the hook. This doesn’t involve any cash out of pocket, and could be attractive if one of you believes the business has value and can support the obligations.
In the future, as part of creating any limited liability companies or other businesses, if you have any partners, you should draft a buy-sell agreement at the outset, delineating what happens if one person wants out and providing a mechanism for that event. A business attorney can help you do this.