Yes, under the right circumstances in both state and federal courts a party can sue an LLC and its owners.
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The facts of the case determine whether the "corporate veil" can be "pierced": http://en.wikipedia.org/wiki/Piercing_the_corporate_veil
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If the LLC had been a Nevada company, under the 'sole remedy' law (in Nevada) the only remedy available under the statute would have been a charging order, which gives the Manager of any Nevada LLC flexibility and 'timing' on his or her side. In addition, if the Members of the LLC were either an irrevocable Multi-Generation Dynasty Trust or a Nevada Asset Protection Trust, the plaintiffs would have most likely NOT have been able to seize any assets.