You are using the term "ownership interest", but I don't know that it applies to an LLC. If you set up the LLC with such stipulations, then possibly it does. But, think of the LLC as similar to a corporation. If you buy a thousand shares in a new corporation and decide you don't want to own the shares any longer, the corporation is not obligated to pay you a portion of what the corporation is worth. You have to go by the rules and try to sell your shares. Who "owns" IBM, Microsoft, or GMAC? No one in particular. If they had to pay a chunk of money from the company everytime someone felt like asking for it, the companies would go under and a corporation, or even an LLC would be worthless.
In an LLC, if you want out, you have to go by the rules. No one is necessarily obligated to pay you a portion of the company's value.
Again, I want to emphasize--this is not a partnership where everyone is an individual owner. You may set up the LLC like that, but it would be foolish to do so. The company would be unstable. Example: What if I wanted to start an LLC as some sort of a Legal Business. Myself and 2 other people put in $50,000 each and registered with the state and all. I buy furniture, rent a building, put advertising out there, hire help, etc. Then, a few weeks later, the other 2 want me to pay them back their money because they changed their mind. The business would be "out of business". That is one of the advantages of these types of business organizations. They can go on even if one of the members does not. He took the chance. I'm not saying he doesn't have something coming, but he needs to go through whatever channels your LLC requires and get paid whatever the members (through the Operating Agreement) decide he has coming.