If there is an agreement or a term in an agreement, such as the shareholders agreement, allowing majority owners of a corporation to force the minority holders to sell at a predetermined price (or a price determined by some other mechanism set forth in the agreement), the majority owners can enforce that agreement. Similar things can be done with a limited liability company, or LLC. While LLCs are not corporations, there are sufficient parallels that many of the same principals apply, as do general contract principals. With LLCs, such an agreement is often called a buy-sell agreement, or it can be written into the operating agreement.
However, in the absence of such an agreement, majority owners cannot force the minority owners to sell. They can, however, make life miserable for the minority owners and so-called "force" them to sell that way.
For a start, if the minority owners are employed by the business, the majority owners can terminate that employment. Since one of the main advantages for minority owners in a small business is employment—buying into a job, in essence—this can deprive the minority owner of the main reason to stay invested. Similarly, if the minority owner has any contracts with the business, as a vendor or a consultant for example, those can be terminated. (Obviously, any terms in any employment or other agreements limiting termination have to be complied with).
The majority owners can use their power to refuse to declare dividends like with a corporation or make distributions such as in a limited liability company, thereby depriving the minority owner of that benefit, too. And the majority owners can, subject to any limitations in any operating agreements, pursue strategies or take actions with which the minority owners disagree. In short, the majority owners can make it so the minority owner wants out. Since the stock or other equity of a small or closely held business is illiquid, they can, within reason, dictate the buy-out price.
There are some protections under the law for minority owners against gross overreaching or abuses by majority owners. The protections are stronger for corporations than for LLCs. Majority owners looking to get rid of a minority owner should consult with a business or corporate lawyer to see what they can do. Minority owners being forced out should likewise consult with an attorney to see about their rights and recourse.